{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization Methods\n",
    "\n",
    "Until now, you've always used Gradient Descent to update the parameters and minimize the cost. In this notebook, you will learn more advanced optimization methods that can speed up learning and perhaps even get you to a better final value for the cost function. Having a good optimization algorithm can be the difference between waiting days vs. just a few hours to get a good result. \n",
    "\n",
    "Gradient descent goes \"downhill\" on a cost function $J$. Think of it as trying to do this: \n",
    "<img src=\"images/cost.jpg\" style=\"width:650px;height:300px;\">\n",
    "<caption><center> <u> **Figure 1** </u>: **Minimizing the cost is like finding the lowest point in a hilly landscape**<br> At each step of the training, you update your parameters following a certain direction to try to get to the lowest possible point. </center></caption>\n",
    "\n",
    "**Notations**: As usual, $\\frac{\\partial J}{\\partial a } = $ `da` for any variable `a`.\n",
    "\n",
    "To get started, run the following code to import the libraries you will need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "import math\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "\n",
    "from opt_utils import load_params_and_grads, initialize_parameters, forward_propagation, backward_propagation\n",
    "from opt_utils import compute_cost, predict, predict_dec, plot_decision_boundary, load_dataset\n",
    "from testCases import *\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plots\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Gradient Descent\n",
    "\n",
    "A simple optimization method in machine learning is gradient descent (GD). When you take gradient steps with respect to all $m$ examples on each step, it is also called Batch Gradient Descent. \n",
    "\n",
    "**Warm-up exercise**: Implement the gradient descent update rule. The  gradient descent rule is, for $l = 1, ..., L$: \n",
    "$$ W^{[l]} = W^{[l]} - \\alpha \\text{ } dW^{[l]} \\tag{1}$$\n",
    "$$ b^{[l]} = b^{[l]} - \\alpha \\text{ } db^{[l]} \\tag{2}$$\n",
    "\n",
    "where L is the number of layers and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary. Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_gd\n",
    "\n",
    "def update_parameters_with_gd(parameters, grads, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using one step of gradient descent\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters to be updated:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients to update each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "\n",
    "    # Update rule for each parameter\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)]-learning_rate*grads['dW' + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] = parameters['b' + str(l+1)]-learning_rate*grads['db' + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.63535156 -0.62320365 -0.53718766]\n",
      " [-1.07799357  0.85639907 -2.29470142]]\n",
      "b1 = [[ 1.74604067]\n",
      " [-0.75184921]]\n",
      "W2 = [[ 0.32171798 -0.25467393  1.46902454]\n",
      " [-2.05617317 -0.31554548 -0.3756023 ]\n",
      " [ 1.1404819  -1.09976462 -0.1612551 ]]\n",
      "b2 = [[-0.88020257]\n",
      " [ 0.02561572]\n",
      " [ 0.57539477]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, learning_rate = update_parameters_with_gd_test_case()\n",
    "\n",
    "parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63535156 -0.62320365 -0.53718766]\n",
    " [-1.07799357  0.85639907 -2.29470142]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74604067]\n",
    " [-0.75184921]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32171798 -0.25467393  1.46902454]\n",
    " [-2.05617317 -0.31554548 -0.3756023 ]\n",
    " [ 1.1404819  -1.09976462 -0.1612551 ]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88020257]\n",
    " [ 0.02561572]\n",
    " [ 0.57539477]] </td> \n",
    "    </tr> \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A variant of this is Stochastic Gradient Descent (SGD), which is equivalent to mini-batch gradient descent where each mini-batch has just 1 example. The update rule that you have just implemented does not change. What changes is that you would be computing gradients on just one training example at a time, rather than on the whole training set. The code examples below illustrate the difference between stochastic gradient descent and (batch) gradient descent. \n",
    "\n",
    "- **(Batch) Gradient Descent**:\n",
    "\n",
    "``` python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    # Forward propagation\n",
    "    a, caches = forward_propagation(X, parameters)\n",
    "    # Compute cost.\n",
    "    cost = compute_cost(a, Y)\n",
    "    # Backward propagation.\n",
    "    grads = backward_propagation(a, caches, parameters)\n",
    "    # Update parameters.\n",
    "    parameters = update_parameters(parameters, grads)\n",
    "        \n",
    "```\n",
    "\n",
    "- **Stochastic Gradient Descent**:\n",
    "\n",
    "```python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    for j in range(0, m):\n",
    "        # Forward propagation\n",
    "        a, caches = forward_propagation(X[:,j], parameters)\n",
    "        # Compute cost\n",
    "        cost = compute_cost(a, Y[:,j])\n",
    "        # Backward propagation\n",
    "        grads = backward_propagation(a, caches, parameters)\n",
    "        # Update parameters.\n",
    "        parameters = update_parameters(parameters, grads)\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Stochastic Gradient Descent, you use only 1 training example before updating the gradients. When the training set is large, SGD can be faster. But the parameters will \"oscillate\" toward the minimum rather than converge smoothly. Here is an illustration of this: \n",
    "\n",
    "<img src=\"images/kiank_sgd.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 1** </u><font color='purple'>  : **SGD vs GD**<br> \"+\" denotes a minimum of the cost. SGD leads to many oscillations to reach convergence. But each step is a lot faster to compute for SGD than for GD, as it uses only one training example (vs. the whole batch for GD). </center></caption>\n",
    "\n",
    "**Note** also that implementing SGD requires 3 for-loops in total:\n",
    "1. Over the number of iterations\n",
    "2. Over the $m$ training examples\n",
    "3. Over the layers (to update all parameters, from $(W^{[1]},b^{[1]})$ to $(W^{[L]},b^{[L]})$)\n",
    "\n",
    "In practice, you'll often get faster results if you do not use neither the whole training set, nor only one training example, to perform each update. Mini-batch gradient descent uses an intermediate number of examples for each step. With mini-batch gradient descent, you loop over the mini-batches instead of looping over individual training examples.\n",
    "\n",
    "<img src=\"images/kiank_minibatch.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 2** </u>: <font color='purple'>  **SGD vs Mini-Batch GD**<br> \"+\" denotes a minimum of the cost. Using mini-batches in your optimization algorithm often leads to faster optimization. </center></caption>\n",
    "\n",
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- The difference between gradient descent, mini-batch gradient descent and stochastic gradient descent is the number of examples you use to perform one update step.\n",
    "- You have to tune a learning rate hyperparameter $\\alpha$.\n",
    "- With a well-turned mini-batch size, usually it outperforms either gradient descent or stochastic gradient descent (particularly when the training set is large)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - Mini-Batch Gradient descent\n",
    "\n",
    "Let's learn how to build mini-batches from the training set (X, Y).\n",
    "\n",
    "There are two steps:\n",
    "- **Shuffle**: Create a shuffled version of the training set (X, Y) as shown below. Each column of X and Y represents a training example. Note that the random shuffling is done synchronously between X and Y. Such that after the shuffling the $i^{th}$ column of X is the example corresponding to the $i^{th}$ label in Y. The shuffling step ensures that examples will be split randomly into different mini-batches. \n",
    "\n",
    "<img src=\"images/kiank_shuffle.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "- **Partition**: Partition the shuffled (X, Y) into mini-batches of size `mini_batch_size` (here 64). Note that the number of training examples is not always divisible by `mini_batch_size`. The last mini batch might be smaller, but you don't need to worry about this. When the final mini-batch is smaller than the full `mini_batch_size`, it will look like this: \n",
    "\n",
    "<img src=\"images/kiank_partition.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "**Exercise**: Implement `random_mini_batches`. We coded the shuffling part for you. To help you with the partitioning step, we give you the following code that selects the indexes for the $1^{st}$ and $2^{nd}$ mini-batches:\n",
    "```python\n",
    "first_mini_batch_X = shuffled_X[:, 0 : mini_batch_size]\n",
    "second_mini_batch_X = shuffled_X[:, mini_batch_size : 2 * mini_batch_size]\n",
    "...\n",
    "```\n",
    "\n",
    "Note that the last mini-batch might end up smaller than `mini_batch_size=64`. Let $\\lfloor s \\rfloor$ represents $s$ rounded down to the nearest integer (this is `math.floor(s)` in Python). If the total number of examples is not a multiple of `mini_batch_size=64` then there will be $\\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$ mini-batches with a full 64 examples, and the number of examples in the final mini-batch will be ($m-mini_\\_batch_\\_size \\times \\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: random_mini_batches\n",
    "\n",
    "def random_mini_batches(X, Y, mini_batch_size = 64, seed = 0):\n",
    "    \"\"\"\n",
    "    Creates a list of random minibatches from (X, Y)\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (input size, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    mini_batch_size -- size of the mini-batches, integer\n",
    "    \n",
    "    Returns:\n",
    "    mini_batches -- list of synchronous (mini_batch_X, mini_batch_Y)\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(seed)            # To make your \"random\" minibatches the same as ours\n",
    "    m = X.shape[1]                  # number of training examples\n",
    "    mini_batches = []\n",
    "        \n",
    "    # Step 1: Shuffle (X, Y)\n",
    "    permutation = list(np.random.permutation(m))\n",
    "    shuffled_X = X[:, permutation]\n",
    "    shuffled_Y = Y[:, permutation].reshape((1,m))\n",
    "\n",
    "    # Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.\n",
    "    num_complete_minibatches = math.floor(m/mini_batch_size) # number of mini batches of size mini_batch_size in your partitionning\n",
    "    for k in range(0, num_complete_minibatches):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, k*mini_batch_size : (k+1)*mini_batch_size]\n",
    "        mini_batch_Y = shuffled_Y[:, 1 : mini_batch_size+1]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    # Handling the end case (last mini-batch < mini_batch_size)\n",
    "    if m % mini_batch_size != 0:\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, num_complete_minibatches*mini_batch_size : m]\n",
    "        mini_batch_Y = shuffled_Y[:, num_complete_minibatches*mini_batch_size : m]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    return mini_batches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of the 1st mini_batch_X: (12288, 64)\n",
      "shape of the 2nd mini_batch_X: (12288, 64)\n",
      "shape of the 3rd mini_batch_X: (12288, 20)\n",
      "shape of the 1st mini_batch_Y: (1, 64)\n",
      "shape of the 2nd mini_batch_Y: (1, 64)\n",
      "shape of the 3rd mini_batch_Y: (1, 20)\n",
      "mini batch sanity check: [ 0.90085595 -0.7612069   0.2344157 ]\n"
     ]
    }
   ],
   "source": [
    "X_assess, Y_assess, mini_batch_size = random_mini_batches_test_case()\n",
    "mini_batches = random_mini_batches(X_assess, Y_assess, mini_batch_size)\n",
    "\n",
    "print (\"shape of the 1st mini_batch_X: \" + str(mini_batches[0][0].shape))\n",
    "print (\"shape of the 2nd mini_batch_X: \" + str(mini_batches[1][0].shape))\n",
    "print (\"shape of the 3rd mini_batch_X: \" + str(mini_batches[2][0].shape))\n",
    "print (\"shape of the 1st mini_batch_Y: \" + str(mini_batches[0][1].shape))\n",
    "print (\"shape of the 2nd mini_batch_Y: \" + str(mini_batches[1][1].shape)) \n",
    "print (\"shape of the 3rd mini_batch_Y: \" + str(mini_batches[2][1].shape))\n",
    "print (\"mini batch sanity check: \" + str(mini_batches[0][0][0][0:3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:50%\"> \n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_X** </td> \n",
    "           <td > (12288, 20) </td> \n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_Y** </td> \n",
    "           <td > (1, 20) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **mini batch sanity check** </td> \n",
    "           <td > [ 0.90085595 -0.7612069   0.2344157 ] </td> \n",
    "    </tr>\n",
    "    \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Shuffling and Partitioning are the two steps required to build mini-batches\n",
    "- Powers of two are often chosen to be the mini-batch size, e.g., 16, 32, 64, 128."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - Momentum\n",
    "\n",
    "Because mini-batch gradient descent makes a parameter update after seeing just a subset of examples, the direction of the update has some variance, and so the path taken by mini-batch gradient descent will \"oscillate\" toward convergence. Using momentum can reduce these oscillations. \n",
    "\n",
    "Momentum takes into account the past gradients to smooth out the update. We will store the 'direction' of the previous gradients in the variable $v$. Formally, this will be the exponentially weighted average of the gradient on previous steps. You can also think of $v$ as the \"velocity\" of a ball rolling downhill, building up speed (and momentum) according to the direction of the gradient/slope of the hill. \n",
    "\n",
    "<img src=\"images/opt_momentum.png\" style=\"width:400px;height:250px;\">\n",
    "<caption><center> <u><font color='purple'>**Figure 3**</u><font color='purple'>: The red arrows shows the direction taken by one step of mini-batch gradient descent with momentum. The blue points show the direction of the gradient (with respect to the current mini-batch) on each step. Rather than just following the gradient, we let the gradient influence $v$ and then take a step in the direction of $v$.<br> <font color='black'> </center>\n",
    "\n",
    "\n",
    "**Exercise**: Initialize the velocity. The velocity, $v$, is a python dictionary that needs to be initialized with arrays of zeros. Its keys are the same as those in the `grads` dictionary, that is:\n",
    "for $l =1,...,L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "```\n",
    "**Note** that the iterator l starts at 0 in the for loop while the first parameters are v[\"dW1\"] and v[\"db1\"] (that's a \"one\" on the superscript). This is why we are shifting l to l+1 in the `for` loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_velocity\n",
    "\n",
    "def initialize_velocity(parameters):\n",
    "    \"\"\"\n",
    "    Initializes the velocity as a python dictionary with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    \n",
    "    Returns:\n",
    "    v -- python dictionary containing the current velocity.\n",
    "                    v['dW' + str(l)] = velocity of dWl\n",
    "                    v['db' + str(l)] = velocity of dbl\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    \n",
    "    # Initialize velocity\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db1\"] = [[0.]\n",
      " [0.]]\n",
      "v[\"dW2\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db2\"] = [[0.]\n",
      " [0.]\n",
      " [0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_velocity_test_case()\n",
    "\n",
    "v = initialize_velocity(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with momentum. The momentum update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$ \\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta v_{dW^{[l]}} + (1 - \\beta) dW^{[l]} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha v_{dW^{[l]}}\n",
    "\\end{cases}\\tag{3}$$\n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{db^{[l]}} = \\beta v_{db^{[l]}} + (1 - \\beta) db^{[l]} \\\\\n",
    "b^{[l]} = b^{[l]} - \\alpha v_{db^{[l]}} \n",
    "\\end{cases}\\tag{4}$$\n",
    "\n",
    "where L is the number of layers, $\\beta$ is the momentum and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary.  Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$ (that's a \"one\" on the superscript). So you will need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_momentum\n",
    "\n",
    "def update_parameters_with_momentum(parameters, grads, v, beta, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using Momentum\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- python dictionary containing the current velocity:\n",
    "                    v['dW' + str(l)] = ...\n",
    "                    v['db' + str(l)] = ...\n",
    "    beta -- the momentum hyperparameter, scalar\n",
    "    learning_rate -- the learning rate, scalar\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- python dictionary containing your updated velocities\n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    \n",
    "    # Momentum update for each parameter\n",
    "    for l in range(L):\n",
    "        \n",
    "        ### START CODE HERE ### (approx. 4 lines)\n",
    "        # compute velocities\n",
    "        v[\"dW\" + str(l+1)] = beta*v[\"dW\" + str(l+1)] + (1-beta)*grads[\"dW\" + str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta*v[\"db\" + str(l+1)] + (1-beta)*grads[\"db\" + str(l+1)]\n",
    "        # update parameters\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)]-learning_rate*v[\"dW\" + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)]-learning_rate*v[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters, v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.62544598 -0.61290114 -0.52907334]\n",
      " [-1.07347112  0.86450677 -2.30085497]]\n",
      "b1 = [[ 1.74493465]\n",
      " [-0.76027113]]\n",
      "W2 = [[ 0.31930698 -0.24990073  1.4627996 ]\n",
      " [-2.05974396 -0.32173003 -0.38320915]\n",
      " [ 1.13444069 -1.0998786  -0.1713109 ]]\n",
      "b2 = [[-0.87809283]\n",
      " [ 0.04055394]\n",
      " [ 0.58207317]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[0.02344157]\n",
      " [0.16598022]\n",
      " [0.07420442]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v = update_parameters_with_momentum_test_case()\n",
    "\n",
    "parameters, v = update_parameters_with_momentum(parameters, grads, v, beta = 0.9, learning_rate = 0.01)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:90%\"> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.62544598 -0.61290114 -0.52907334]\n",
    " [-1.07347112  0.86450677 -2.30085497]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74493465]\n",
    " [-0.76027113]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.31930698 -0.24990073  1.4627996 ]\n",
    " [-2.05974396 -0.32173003 -0.38320915]\n",
    " [ 1.13444069 -1.0998786  -0.1713109 ]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.87809283]\n",
    " [ 0.04055394]\n",
    " [ 0.58207317]] </td> \n",
    "    </tr> \n",
    "\n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]]</td> \n",
    "    </tr> \n",
    "</table>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Note** that:\n",
    "- The velocity is initialized with zeros. So the algorithm will take a few iterations to \"build up\" velocity and start to take bigger steps.\n",
    "- If $\\beta = 0$, then this just becomes standard gradient descent without momentum. \n",
    "\n",
    "**How do you choose $\\beta$?**\n",
    "\n",
    "- The larger the momentum $\\beta$ is, the smoother the update because the more we take the past gradients into account. But if $\\beta$ is too big, it could also smooth out the updates too much. \n",
    "- Common values for $\\beta$ range from 0.8 to 0.999. If you don't feel inclined to tune this, $\\beta = 0.9$ is often a reasonable default. \n",
    "- Tuning the optimal $\\beta$ for your model might need trying several values to see what works best in term of reducing the value of the cost function $J$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Momentum takes past gradients into account to smooth out the steps of gradient descent. It can be applied with batch gradient descent, mini-batch gradient descent or stochastic gradient descent.\n",
    "- You have to tune a momentum hyperparameter $\\beta$ and a learning rate $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 - Adam\n",
    "\n",
    "Adam is one of the most effective optimization algorithms for training neural networks. It combines ideas from RMSProp (described in lecture) and Momentum. \n",
    "\n",
    "**How does Adam work?**\n",
    "1. It calculates an exponentially weighted average of past gradients, and stores it in variables $v$ (before bias correction) and $v^{corrected}$ (with bias correction). \n",
    "2. It calculates an exponentially weighted average of the squares of the past gradients, and  stores it in variables $s$ (before bias correction) and $s^{corrected}$ (with bias correction). \n",
    "3. It updates parameters in a direction based on combining information from \"1\" and \"2\".\n",
    "\n",
    "The update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta_1 v_{dW^{[l]}} + (1 - \\beta_1) \\frac{\\partial \\mathcal{J} }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{dW^{[l]}} = \\frac{v_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{dW^{[l]}} = \\beta_2 s_{dW^{[l]}} + (1 - \\beta_2) (\\frac{\\partial \\mathcal{J} }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{dW^{[l]}} = \\frac{s_{dW^{[l]}}}{1 - (\\beta_2)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{dW^{[l]}}}{\\sqrt{s^{corrected}_{dW^{[l]}}} + \\varepsilon}\n",
    "\\end{cases}$$\n",
    "where:\n",
    "- t counts the number of steps taken of Adam \n",
    "- L is the number of layers\n",
    "- $\\beta_1$ and $\\beta_2$ are hyperparameters that control the two exponentially weighted averages. \n",
    "- $\\alpha$ is the learning rate\n",
    "- $\\varepsilon$ is a very small number to avoid dividing by zero\n",
    "\n",
    "As usual, we will store all parameters in the `parameters` dictionary  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**: Initialize the Adam variables $v, s$ which keep track of the past information.\n",
    "\n",
    "**Instruction**: The variables $v, s$ are python dictionaries that need to be initialized with arrays of zeros. Their keys are the same as for `grads`, that is:\n",
    "for $l = 1, ..., L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "s[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "s[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_adam\n",
    "\n",
    "def initialize_adam(parameters) :\n",
    "    \"\"\"\n",
    "    Initializes v and s as two python dictionaries with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters[\"W\" + str(l)] = Wl\n",
    "                    parameters[\"b\" + str(l)] = bl\n",
    "    \n",
    "    Returns: \n",
    "    v -- python dictionary that will contain the exponentially weighted average of the gradient.\n",
    "                    v[\"dW\" + str(l)] = ...\n",
    "                    v[\"db\" + str(l)] = ...\n",
    "    s -- python dictionary that will contain the exponentially weighted average of the squared gradient.\n",
    "                    s[\"dW\" + str(l)] = ...\n",
    "                    s[\"db\" + str(l)] = ...\n",
    "\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    s = {}\n",
    "    \n",
    "    # Initialize v, s. Input: \"parameters\". Outputs: \"v, s\".\n",
    "    for l in range(L):\n",
    "    ### START CODE HERE ### (approx. 4 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "        s[\"dW\" + str(l+1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        s[\"db\" + str(l+1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    return v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db1\"] = [[0.]\n",
      " [0.]]\n",
      "v[\"dW2\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db2\"] = [[0.]\n",
      " [0.]\n",
      " [0.]]\n",
      "s[\"dW1\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "s[\"db1\"] = [[0.]\n",
      " [0.]]\n",
      "s[\"dW2\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "s[\"db2\"] = [[0.]\n",
      " [0.]\n",
      " [0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_adam_test_case()\n",
    "\n",
    "v, s = initialize_adam(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr>\n",
    "\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with Adam. Recall the general update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{W^{[l]}} = \\beta_1 v_{W^{[l]}} + (1 - \\beta_1) \\frac{\\partial J }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{W^{[l]}} = \\frac{v_{W^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{W^{[l]}} = \\beta_2 s_{W^{[l]}} + (1 - \\beta_2) (\\frac{\\partial J }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{W^{[l]}} = \\frac{s_{W^{[l]}}}{1 - (\\beta_2)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{W^{[l]}}}{\\sqrt{s^{corrected}_{W^{[l]}}}+\\varepsilon}\n",
    "\\end{cases}$$\n",
    "\n",
    "\n",
    "**Note** that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_adam\n",
    "\n",
    "def update_parameters_with_adam(parameters, grads, v, s, t, learning_rate = 0.01,\n",
    "                                beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8):\n",
    "    \"\"\"\n",
    "    Update parameters using Adam\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    beta1 -- Exponential decay hyperparameter for the first moment estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the second moment estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2                 # number of layers in the neural networks\n",
    "    v_corrected = {}                         # Initializing first moment estimate, python dictionary\n",
    "    s_corrected = {}                         # Initializing second moment estimate, python dictionary\n",
    "    \n",
    "    # Perform Adam update on all parameters\n",
    "    for l in range(L):\n",
    "        # Moving average of the gradients. Inputs: \"v, grads, beta1\". Output: \"v\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = beta1*v[\"dW\" + str(l+1)] + (1-beta1)*grads['dW' + str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta1*v[\"db\" + str(l+1)] + (1-beta1)*grads['db' + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected first moment estimate. Inputs: \"v, beta1, t\". Output: \"v_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v_corrected[\"dW\" + str(l+1)] = v[\"dW\" + str(l+1)]/(1-beta1**t)\n",
    "        v_corrected[\"db\" + str(l+1)] = v[\"db\" + str(l+1)]/(1-beta1**t)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Moving average of the squared gradients. Inputs: \"s, grads, beta2\". Output: \"s\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s[\"dW\" + str(l+1)] = beta2*s[\"dW\" + str(l+1)] + (1-beta2)*(grads['dW' + str(l+1)]**2)\n",
    "        s[\"db\" + str(l+1)] = beta2*s[\"db\" + str(l+1)] + (1-beta2)*(grads['db' + str(l+1)]**2)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected second raw moment estimate. Inputs: \"s, beta2, t\". Output: \"s_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s_corrected[\"dW\" + str(l+1)] = s[\"dW\" + str(l+1)]/(1-beta2**t)\n",
    "        s_corrected[\"db\" + str(l+1)] = s[\"db\" + str(l+1)]/(1-beta2**t)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Update parameters. Inputs: \"parameters, learning_rate, v_corrected, s_corrected, epsilon\". Output: \"parameters\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] - learning_rate * ( v_corrected[\"dW\" + str(l+1)] / (np.sqrt(s_corrected[\"dW\" + str(l+1)]) + epsilon))\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] - learning_rate * ( v_corrected[\"db\" + str(l+1)] / (np.sqrt(s_corrected[\"db\" + str(l+1)]) + epsilon))\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "    return parameters, v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.63178673 -0.61919778 -0.53561312]\n",
      " [-1.08040999  0.85796626 -2.29409733]]\n",
      "b1 = [[ 1.75225313]\n",
      " [-0.75376553]]\n",
      "W2 = [[ 0.32648046 -0.25681174  1.46954931]\n",
      " [-2.05269934 -0.31497584 -0.37661299]\n",
      " [ 1.14121081 -1.09244991 -0.16498684]]\n",
      "b2 = [[-0.88529979]\n",
      " [ 0.03477238]\n",
      " [ 0.57537385]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[0.02344157]\n",
      " [0.16598022]\n",
      " [0.07420442]]\n",
      "s[\"dW1\"] = [[0.00121136 0.00131039 0.00081287]\n",
      " [0.0002525  0.00081154 0.00046748]]\n",
      "s[\"db1\"] = [[1.51020075e-05]\n",
      " [8.75664434e-04]]\n",
      "s[\"dW2\"] = [[7.17640232e-05 2.81276921e-04 4.78394595e-04]\n",
      " [1.57413361e-04 4.72206320e-04 7.14372576e-04]\n",
      " [4.50571368e-04 1.60392066e-07 1.24838242e-03]]\n",
      "s[\"db2\"] = [[5.49507194e-05]\n",
      " [2.75494327e-03]\n",
      " [5.50629536e-04]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v, s = update_parameters_with_adam_test_case()\n",
    "parameters, v, s  = update_parameters_with_adam(parameters, grads, v, s, t = 2)\n",
    "\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63178673 -0.61919778 -0.53561312]\n",
    " [-1.08040999  0.85796626 -2.29409733]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.75225313]\n",
    " [-0.75376553]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32648046 -0.25681174  1.46954931]\n",
    " [-2.05269934 -0.31497584 -0.37661299]\n",
    " [ 1.14121081 -1.09245036 -0.16498684]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88529978]\n",
    " [ 0.03477238]\n",
    " [ 0.57537385]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.00121136  0.00131039  0.00081287]\n",
    " [ 0.0002525   0.00081154  0.00046748]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[  1.51020075e-05]\n",
    " [  8.75664434e-04]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[  7.17640232e-05   2.81276921e-04   4.78394595e-04]\n",
    " [  1.57413361e-04   4.72206320e-04   7.14372576e-04]\n",
    " [  4.50571368e-04   1.60392066e-07   1.24838242e-03]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[  5.49507194e-05]\n",
    " [  2.75494327e-03]\n",
    " [  5.50629536e-04]] </td> \n",
    "    </tr>\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You now have three working optimization algorithms (mini-batch gradient descent, Momentum, Adam). Let's implement a model with each of these optimizers and observe the difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 - Model with different optimization algorithms\n",
    "\n",
    "Lets use the following \"moons\" dataset to test the different optimization methods. (The dataset is named \"moons\" because the data from each of the two classes looks a bit like a crescent-shaped moon.) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_X, train_Y = load_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have already implemented a 3-layer neural network. You will train it with: \n",
    "- Mini-batch **Gradient Descent**: it will call your function:\n",
    "    - `update_parameters_with_gd()`\n",
    "- Mini-batch **Momentum**: it will call your functions:\n",
    "    - `initialize_velocity()` and `update_parameters_with_momentum()`\n",
    "- Mini-batch **Adam**: it will call your functions:\n",
    "    - `initialize_adam()` and `update_parameters_with_adam()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(X, Y, layers_dims, optimizer, learning_rate = 0.0007, mini_batch_size = 64, beta = 0.9,\n",
    "          beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8, num_epochs = 10000, print_cost = True):\n",
    "    \"\"\"\n",
    "    3-layer neural network model which can be run in different optimizer modes.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (2, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    layers_dims -- python list, containing the size of each layer\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    mini_batch_size -- the size of a mini batch\n",
    "    beta -- Momentum hyperparameter\n",
    "    beta1 -- Exponential decay hyperparameter for the past gradients estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the past squared gradients estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "    num_epochs -- number of epochs\n",
    "    print_cost -- True to print the cost every 1000 epochs\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(layers_dims)             # number of layers in the neural networks\n",
    "    costs = []                       # to keep track of the cost\n",
    "    t = 0                            # initializing the counter required for Adam update\n",
    "    seed = 10                        # For grading purposes, so that your \"random\" minibatches are the same as ours\n",
    "    \n",
    "    # Initialize parameters\n",
    "    parameters = initialize_parameters(layers_dims)\n",
    "\n",
    "    # Initialize the optimizer\n",
    "    if optimizer == \"gd\":\n",
    "        pass # no initialization required for gradient descent\n",
    "    elif optimizer == \"momentum\":\n",
    "        v = initialize_velocity(parameters)\n",
    "    elif optimizer == \"adam\":\n",
    "        v, s = initialize_adam(parameters)\n",
    "    \n",
    "    # Optimization loop\n",
    "    for i in range(num_epochs):\n",
    "        \n",
    "        # Define the random minibatches. We increment the seed to reshuffle differently the dataset after each epoch\n",
    "        seed = seed + 1\n",
    "        minibatches = random_mini_batches(X, Y, mini_batch_size, seed)\n",
    "\n",
    "        for minibatch in minibatches:\n",
    "\n",
    "            # Select a minibatch\n",
    "            (minibatch_X, minibatch_Y) = minibatch\n",
    "\n",
    "            # Forward propagation\n",
    "            a3, caches = forward_propagation(minibatch_X, parameters)\n",
    "\n",
    "            # Compute cost\n",
    "            cost = compute_cost(a3, minibatch_Y)\n",
    "\n",
    "            # Backward propagation\n",
    "            grads = backward_propagation(minibatch_X, minibatch_Y, caches)\n",
    "\n",
    "            # Update parameters\n",
    "            if optimizer == \"gd\":\n",
    "                parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "            elif optimizer == \"momentum\":\n",
    "                parameters, v = update_parameters_with_momentum(parameters, grads, v, beta, learning_rate)\n",
    "            elif optimizer == \"adam\":\n",
    "                t = t + 1 # Adam counter\n",
    "                parameters, v, s = update_parameters_with_adam(parameters, grads, v, s,\n",
    "                                                               t, learning_rate, beta1, beta2,  epsilon)\n",
    "        \n",
    "        # Print the cost every 1000 epoch\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            print (\"Cost after epoch %i: %f\" %(i, cost))\n",
    "        if print_cost and i % 100 == 0:\n",
    "            costs.append(cost)\n",
    "                \n",
    "    # plot the cost\n",
    "    plt.plot(costs)\n",
    "    plt.ylabel('cost')\n",
    "    plt.xlabel('epochs (per 100)')\n",
    "    plt.title(\"Learning rate = \" + str(learning_rate))\n",
    "    plt.show()\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will now run this 3 layer neural network with each of the 3 optimization methods.\n",
    "\n",
    "### 5.1 - Mini-batch Gradient descent\n",
    "\n",
    "Run the following code to see how the model does with mini-batch gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690746\n",
      "Cost after epoch 1000: 0.716034\n",
      "Cost after epoch 2000: 0.685675\n",
      "Cost after epoch 3000: 0.687649\n",
      "Cost after epoch 4000: 0.693756\n",
      "Cost after epoch 5000: 0.688294\n",
      "Cost after epoch 6000: 0.681137\n",
      "Cost after epoch 7000: 0.682902\n",
      "Cost after epoch 8000: 0.668747\n",
      "Cost after epoch 9000: 0.663290\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.6666666666666666\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"gd\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Gradient Descent optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.2 - Mini-batch gradient descent with momentum\n",
    "\n",
    "Run the following code to see how the model does with momentum. Because this example is relatively simple, the gains from using momemtum are small; but for more complex problems you might see bigger gains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690743\n",
      "Cost after epoch 1000: 0.716043\n",
      "Cost after epoch 2000: 0.685671\n",
      "Cost after epoch 3000: 0.687635\n",
      "Cost after epoch 4000: 0.693785\n",
      "Cost after epoch 5000: 0.688294\n",
      "Cost after epoch 6000: 0.681130\n",
      "Cost after epoch 7000: 0.682888\n",
      "Cost after epoch 8000: 0.668739\n",
      "Cost after epoch 9000: 0.663289\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.6666666666666666\n"
     ]
    },
    {
     "data": {
      "image/png": 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466VXqGlvByHoWLKEPY8+TLxkDos6CkHnksXUN7dkOiICWELQ3tg4KyKcvnkroapK1r+/n0AkStvyZZy49RYSRcFZOb/L9Y2rSFymTCppMdBnkExJAgGFiiqN3i49x/iQEjbv2cuZrVvyOt1LBgapbW0lEQzSvqwxq3e7lkzx2A+fwhuP26a0lDQ0NfHoD5/i2a98eU77vL/30AM8/v0foRgGHsNA1zRMj4d9D8yeX6h9WSPtyxrtD1JSPBTCH425ysRlxnEVicuUiEVNWptSGaWRiFkMDhh5Q4C9iQSqYWB6PNkrpOS2115n5fGTSCGQQmB4PLzy658gVFUFwLLTp1ENI2s+VpESXyLOwouXaF254soCS2mfX9OmNYIsXFHBz7/yZVYcO05FTw/9dXVcuHF9wbXCSvv6KA6F6a+tnfLAX9/UzLZfvYQvkUBISU9DPTuffGJurTaXaxpXkbhMic72bMtDSpAmCAWkg9tAAe7/6c/Z89gjRMvKMssbT59hxYlTWSXktVSK+3/2C5797S+BEJT29ePR9dxjmpZjj/QspGTN4SNs3rMXbyJBMuDn8N3bOLdp40QvOS8pv59TE/RJeBMJ7vvZs1R1dWOqCqphcmbzJg7ct2NSiq54cJD7fv4sHn3kPta2tfPQj3/Cc1/+4qyFX7tcX7jOdpdJY5oSPZWvOmP+MauutY3HfvBUlrN8zeEjOUpCAQLRKGV9/QD019ehj7VksIs8DtTUjCvr6g+OctPbO/HH4yhSEojFueWNt1h+7ERmG08yydLTZ1h28hS+eHzc400X2154keqOTjTDwJdMoZkmqz84yspjxyd1vNVHPkAxszW4IiVF4TA1be3TIbKLSw6uReIyaYSw/zkFYqmaoK7BQ2dbirEJ5oqUaKkUS86d5/K6tQBounMElhSgpRVM0+pVbN69ByUUziTfGarKUFUlnUsWjyvrpj178YyJ8vIYBlv27OHihvUsOn+B7c+/gBQKSIkiLd574H4Mr5cVJ04iEVzYsJ7mVSun7a3em0iwoKk5J5HQYxjccOAQ5zdumPAxSwaHco4H9n0sCofpmbS0Li75cRXJNYJlSQb6DEJDJkJAWblKeaWGmMGpDEURFJeoRMJmljIRAioqVYpLbBn6enKVhGYYlAwOZT5fWreW8r6+rKktAKmo9NfVAnYDrBc/9xm2vrOLpWfPAdBXV8uJW28ZX1ApCUajjquC4QjeeJx7fvlCzrnvfOU1TFXNKKCGpiaa1qxmz+OPjn++AvEkU8g83483kZjUMTuXLGbhpUtZU1sAimXR2zBDpWFcrnvcqa1rACklLZeTmaq7yYSkp8ugrSU14+euW+DBH1AQAhTFViIlpSoVVfY7is+vIByeMlPT6K8dmY46s2UTg1WVmakrU1EwNI1djz+aFY2VDAbZf/99DFZXoVgWNe0d7HjueZ78l+/hzTcdJQThMuf+JuHycpacO+84oAsps6wYj2Gw4sRJGi5euuJ9KYRoaQkpB2e8qQjali+b1DEv3LieZCCIOeqe6ZrGpbVriZSXT1pWF5fxcBXJNUA0YpFMyhyndyxikYg7J8pNF6oqWLLMx9IVPhoWeVm2yk/DIm/GEiouUfB4hF2vI43iEYTLy0ZCVQHT4+Glz32GvQ8/yPn1N3D81pt57ktfpG3F8pxzbtm1m6rOLrsciWGXIynr7+f2V1/PK+fBe7ZjjOmQaGgaB3dsRzMMhEOBx3zc9fKrBW87LkLw7iMPYWgaVvp+GapKyu/ng7vusLdJTwPmS3gci+H18sJvfI7TW7cQLi1loLqKA/fu4N1HH54emV1cHHCntq4BYlHTMUJKAvGYhT8w8+8LPp+CU6SrELai6e3SCYVMBLD6I7X8YMEncvI+LFXl0g3ruHTDunHPteL4iZw+I6plseTceYRlOeaTNK1dg6UqbN25h+KhIULl5Rzevo3WlSvY+tbbjn4FJwR2bavS/n5ClZWZ5ctOnGTT3vcIhiP019Vy8J7t9CxccMXjta1Yzq8+/xlu2H+QksFBOpcs5vTWLSSDQRafPcetb7xFMBrFVFVOb9nM4e3brpgvkwwEOHDfDjvyy8VlFnAVyTWApglHp7cQoM7yN2wakkTCQtMEPr894KmqoG6Bl7r0uHrb1xvRfzb5Xuz5yo4IKcctwdKyahUtq1ZlLSvt72fd4Q8YO7E1XiEXKQS++IgPY+3BQ2zduSvjl6hrbeOhH/+EVz79ScLl5Wx89z2Wnj2HoWmc2byR0zdtzVIGgzU1vPvYI1nnqGtuYfsLL2b8NoplsfbQYTRD5/0H7h9HOheX2cdVJNcApeUavT1GzuinCCguUWdFBiklfT0G/b1GRql5fYJFS31o2vQ6/FuXL2fp2XPZ5UiA7oULkerErndx2ooZi0xfhJPkimVl/DvCsti8+90c57ZqGGx9eyfFoTDB8EiU2ZZde6ht6+Cdjzw5rlyb3t2b4/z3GAarjh7j0Pa7MbwzW5rexWUiuD6SawBNEyxe6mU4WVsI8HgFixt9KMrsJKBFwhb9vXZnRMuyFUkyIWlrTuZsu/dLR/n7r3dO+lwH7r2HpM+HkVYahqah+3zsfXgSVXbzRE0NZ9c7MVRZkcnM90djOVV/wZ4Cq+7swh+LZU2beQyDRRcvUtbXN65YpQMDeeRSCOSJQHNxmStci+QaIRBUWb7aTyplv0V7vGJGQ3/HMtCX214XbGWi6xYez8g7Sypp0fZrr/P5Xd2Ymsb5Des5eM/23LIpDpT29XP/z36e8ZFYisLl1avYf/+9pAIBeyMpqezqJhCN0ttQTzKYv+RI0+rVbN69xzZpRiGFIBEMEoxEst62DFXl8Pa7R64v4M87DWaqKn6HMF4pBFUdnQylS7840VdXRyAccXzTi85APxUXl6ngKpKrjETCordLJ5Gw8HgEVTWezPSVEAKfb25KYJhGnuFUgGnCsI4wDEnTxSTWhS4UCYqus+qDY5T19fPapz4x7jmEZfHQj39CYMzg3nj2HCduv5VUIEAwHOaBZ35GcSiEFALFNDl5y00cvnubo/URKS/jwI57uPmtdzLyImH/fTvoXryIB5/+iT3FJCWKZXF66xZaRtX0sjSN01u3sPbQ4axQYUPTaFvWSOPZczkWixRcsbnWkbvupOFyU1b2v+7ROHb7rVia+7N1mV/M6RMphPgO8ATQLaW80WG9AL4JPAbEgC9KKQ/NrpTzh0TcovlSclRpdkl7S4q6Bg9lFXM7uBSVKKT6zRw/jYAs5TbYn7ZcRm2nmSa1be2U9/QwOE6pk7qWFjypVM5bumKarDpylP0P3MeOZ39JWX9/lv9k3cHD9NXV0bxmteNxz2zdQuvKFSw+dx6A5lUriZXaeSc//b3foaGpGV8sTtfihZnlozm8fRuWonDDwUMopkkyEGD/vffQvXgRS85fyFIklhAkgkVXzMQfqKvllU9/ipvffoeqzi7iRUGO3X4b5zfk/ExcXOacuX61+VfgW8D38qx/FFiV/ncb8P+l/78u6el2Ls3e06VTWq7O6lTWWCqrPYSHTExzJHBKCKhr8GTJlUhYjlNglqJQ1tc/riIZHSk1GkVKgpEIRUNDVPT2ZikRAI+uc8PBQ3kVCdg93p16uUtFycp3cUIqCke2b+ODbXei6Tq615uxfl775Me5+4WXCEQjCAk9DfXsevLxgsqs9DXU88qnP3XF7Vxc5po5VSRSyp1CiMZxNvkw8D0ppQTeE0KUCyEapJQdsyLgPCNfcqFl2dNHcznjoWmCxpV+BvsNohELzSOorNJyclj8foVYJFeZKJbFUFUl49G9cCGKg2Nb93hoXbkCbyLp2LscwJtHCTkiJfXNLQSiUXoWLCBSXnblfbAVytiy8T0LF/Lzr3yZYCSCqarj+mtcXK5W5toiuRILgZZRn1vTy7IUiRDiK8BXAOo8gVkTbrbRNEHKdPZFzGFPpwyqavtsqsYpxFteqeU45g1VpWdBw7jWCEC8pJiTN29l3aHDmXBbQ9MIVZRzae2avJFWpqrSvHplQddQPDjEw0//GF8igcQuUX9+w3r2PfjA5Is1CnFFn4iLy9XMfFckTr/cnJFUSvlt4NsAawPl09MUfJ5h6BKfT5BKZl+eEFBWoWaF+SbidiiurlsEixQqqjzTnssxWTRNsGS5j+52nWhCYioq529cz4F77ylo/8Pb76Zn4UK77HwqxeW1azi3cUPGAb334QfZ9uLLKKaJIiWGphEPBgvuXX7vs88RDEeypsdWnDhJ98JFXFo/fsa9i8v1ynxXJK3AaK/kIuC6a6ow3IVwLEJAablKbf1I2GxoyKCjdaSvRzJhMjRg0rjCj+aZH8rE51NYvMyH782P8kd/1zCxnYWgdeWKvN0Qm9auIVRRwbpDhykKhWhbvoxzGzcU1KmweHCQ0oEBBx+LwdpDh11F4uKSh/muSH4JfE0I8TS2k33oevOPSClpb005OqiralSqakYynC3LorMtuzmUlLb/pLdHp37B/MqGTt73LDz+e1nLlp4+w5ZdeygOhQiVl3PonrsdlYY/GqW0f4BweXlOC9mButpJFSn0xhN5iyN6UjNfSdnF5WplrsN/nwJ2ANVCiFbg3wIeACnlPwEvYof+nscO//3NuZF07kglZd7+5+EhK8sf0dmWG9U1TDSSPUBapqSvVyc0ZGWmxyorNcQsZcKDPUfpjeuohkXKr7Hk7BnufPnVTLJhRV8f9z77HLsef5TL6UKOwrK445VXWX7yNKaqopgmLStXsPvxR6eWXyElt775FoqDIjEUhcvr1kz+2C4u1zhzHbX16Susl8Dvz5I485Lx/Luj15mmJBLOX8F2dAkqKSVNl5LoqZHS833dBrGIxaKldgn4eMykq0MnmZAoKlRUalTVTF+jrKga4IUFO6hrDmWSAKs6wjnJe4qUbHvxZVpWrcT0eNjw3j6WnTqDapqZbRdfuMjWd3Zx4P57Jy1PQ1Mzld09jsUbE0VFnLzpJsDuI7/6yFGWnj1L0u/n9NYttE+yd8jVjDeRYNUHx6hrbWWwqpIzWzYTLSssus3l2mO+T21d93i8As0jcnqjCwFllSNfn56SedveAlRWj2wbDplZSgTs/eIxi0RcgrBovjQylWOZ0N9rYBqSummaHnu1/k6GtGKUUcmJffVL6VrUQX3rhaxtFcti+YmTnNu8iXUHD+cUM9QMg9VHj9ll0yep6Ko7OlDH9Iwf5vyG9Rg+L6qu8/j3f0Tx0FBGhvqWFo7feitHh/uHXAcEw2Ge+O4P8KRSaIbBgkuXWXv4A1775MfpWbhwrsVzmQPmQdCoy3gIIVi42IuqglBGijIWlyiUlY+YGR6vyKtEPOn8uFjUREpJPOacFCgldHemaL6Y6w+QEoYGTcw84ccTIaoG6PNW5PYj0Ty0Ls91aAugobnZvpY8vgpN1+0y8pMkXlzsWOvL8Hgyb9orjp+gaJQSAdsRv/G9ffhisUmf+2pjy87d+OLxzH1QLQuPrnPXS6/MsWQuc4WrSOYxUkqklPj8CstX+2lY4KWmzsOS5T4WLPZlTTOpqqCsQnV8IddTtv+ktTnFhTN2Yl6+F/dEPP9gLAQ5ltFkSCkaYmyVxDSmljuYW0IQSQ/mPQsaHIsk9tfWXLHh03hcXrMaS1Wyji1JF4VMZ8QvPn8hq55WRmZVpab9+okBWXTxUk5kG9g5ONeTQnUZwVUk85BY1OTS+QRnTyY4fzpBT1fK7oVeZvdC9/udv7baeg9VNVrGH+IdVePKskCmM+BDg4W3lR2NZcHggEE4ZFs2k6VMj+BxiCCwgIqethxFYWoqZzdtAuD9++/F8Hgw00EBlhDoHo19D06t2ZPh9fLypz/FUFUlhqZhaBpDlZW88ulPZXp/xIuLMy1xRyOkJBm4dhNhx6KPU6XZ6UXA5drH9ZHMMxJxi9amkXBfy4KBPhPTgPqF4/snhBjOLLd/zF3tKVJJZ6VRU6cx0G9i6PaJNA0ME8eWvaMZGjAJDZn4vILFyybX70RBsqPnfV6ruxNTKEihYAkwNYWjd2ykoreZiu4epCLQfT52Pf5opkzJQG0tz3/xC9ywfz/VnV0M1NRw/NabCY1Tkr1QBmtqeO7Lv0lRKATY9beH2+U7AAAgAElEQVRGc3rLZpadOp1VkddKl5vvWTDBfJgZQjEM1h46wooTJ5GK4OzGDZzbtHFK1tpYTm/dbDfzGnUfTEWhbdkyDK+rSK5HxFTeLOcjawPl8jsrt821GJOmrSVJJJQ7mgsBK1b7USeQod7WnHSM5BIK1C/wUFKqYhgSgQABF88mxutUmyNPVY2WUVqTYdBTwonSlby/aD2JoIdIuR+ZVkzBcBhVNwhXlGfm4YpCIRZcvIzp0WhZuaKgJMPpZsWx49z2+ptIIRBSEisp5o2Pf8yWc44RlsUjP/oxld3dGf+Frml0NC7hrY99dFrPs+2Fl1hy7hyWqiKkZKiyktc/+fHryjK71njnG48flFIWVgJiDK5FMs9IJZxHciFA12XBisSyJLFYHvNCQjBoVwv2jMp2LylVCA1l75MvEkxKCA2ZU1Ik5XqYu/oO82/evo8dfxLPWje2NtWGd/eyce8+u5aWENz+6mu8/ZEPX7Ey73RzYcONXF67hqrOLnSfj4Ga6snX4HJidOnkCbLg0mUqenqygwEMg4amFqo7OuhtKNxqquroZMuu3VR1dRMpK+XIXXfStmK5LaKisOtDj1MyMEhFdzeRsjL662qn9z64XFW4imSe4fMrpFK501FS2pFZhRIOmXkTGUvKlJxyKf29OuGQlaM4xrNQpmvYiP3xN0D5w7zrq9s72Pje+5lExWF2/OKXPPP7vzvr0ymmx0P34kXTesyy3j5uf/V16traMBWFi+tvYP99OybUm72upRWPQwizYprUtrYXrEiqOzp4+KlnUA0DAfjjcXY89zx7H3qAizeuz2wXriifF5aYy9zjOtvnGXbSX/ay4cxzVS186I5H8zvU/QE163M4ZNLbbVfkncjUVlmFeuUNp4EVx084lo+XQrDg8uVZkWEm8UejPPbDp6htbUVIiWaaLD9xkvt/+vMJHSdWUozhkN1vqirxosLL1299ZxdaWokMoxkGN7+9s/AHxOW6wlUk8wyfX2Fxow9/wP4Zq6qtXEYXZiyERDLPFJkC3jHWSF9P/tIqjscQECxWKK+cHYNWMU3HHBEhpaOCudpYfeQoimFk/Rg106Sqs4uK7u6Cj3Np3dqcMvoSkKpK86rCyugDVHV1OS73JpP4HHrQu7i4U1tzhJQSw7D7iIy1NAJBhaXL/ZM+djxu5fW1qIqtBEaTt9+6A0XFCtW1npyGVVPhyEsaPJ5/fdPaNSw7fSZn2kZIi47GpdMmx3TgSSS45c23WXb6DMKyaF/WyL4H7mPRhYusf/8AvkSCngULOHDv9kz/lcqurpxpO7B9EWV9/QzU1hZ07mQwyGuf/DXu+eXzeBNJkJJ4cTFvffRDjsmW+YgVl+BN9uUstxRBagJTbS7XD64imQOiEZPOdj0zgAeCCg2LvNPWMyQaNvNaGKXlufWyAkGVcOjKb/bDkVrTqUSGeevju7n3Z87Rdu2NS2lZuYLF5y+g6jpSEUhF5f37751fUUJS8vDTz1De24eaLv648OIlPvy//hUgEy674PJlHvtBG8//xucJV1bQV1/PwsuX0YwxdcYsi8Hq6gmJ0LNwAT/96lco6+tHKoJQRcWEneBH7rqDu158OSu8V9c0Tm/ZglRnZzrT5erCVSSzTCpp0dacXRY+FrVobUqydLkvZ5CfDIoqHKOthMCxJ0l1rUY0YpKngnpm36JiJUuJSCnp7zXo6zWQlm1dVddqVFRNs/NbCHY98Rh1La0sOXce3ePh4vobCF2hNe9sU9fSSunAYEaJgF10UozxNwhANQw2vPce7z72KGc3b2T9/gMohpmZ3jJUle6FCxissRWJLxZj0569LDl3HlPTOLNlE6du2uqcHyIEQ9WTz6tpWrsGXyzG1l17MoUxz27exOHttqJXdZ01h4+w7NRpDI+HM1s2c3ntGjdq6zrGVSSzzEC/4WgtpJKSZEJmfCNTobRUpbfLuQBhSWnuG6XXp7B0hY++boN4zELzCiqrVCzLTkAE27FeUqpmKbrOtlRWuLBlQXengWlKqmuneQpECLqWLKZryeL820iJP6rji+uYmkq01ItUswdaVbfwJnQsVSEZ0KZ18Cvv63P25Thsq0hJdYfti0gGg/zq85/l1jfepKGpGUtRMDwealvb+PA//wtH77ydrTt3E4hEMkpq86491LR18M5Hnpw2+UdzdusWzm3ehD8aIxnwZ0r0K6bJoz98irL+gUyYcVVXN3Utrex76IEZkcVl/uMqklkmX62q4TwR/zTM1ESjzlNbCxblb7nr9drTa2MpLXN+RAxD5uScDNPfa1JVLWe1t4mwJLXNIbxJAyFBCqjoidG5pBTdr4GUlHfHKBlMZMrWm5pC15JSTM/0TNcMVVY69oyX5CoTCwhVVmQ+hysreOMTH2fBpcvc++xzBOJ2Xk15fz93vfgyUkrUUV+qxzBYdPEiZX19DE1DVr8TUlFymoYtPX2W0oHBMYUrdVYeP86JW28mUu6GA08bUl41Vp4btTXLBIKK47MhJfj9U39oLEvS1e5sjUxngFMinn8eTEpb0UyEvV86yt9/vXPS8pT0x/EmDRRpD9olQwMsvHiadftPIAyDYDhFyWACRYJigSJB0y1qW8OTPudYOpcsJlxehjlquskSAlNVc8JypaIQLi/PKXJ409s7c8rkq5aF5vBmIIWgqtM5wmqmWHjpkmOuihQKta1tsyrLNYmUlPbGWHS2nyVn+llwYQB/ZP5353QtkhlESkk4ZNLfa2CZdrRURaXGQL+BOWqsGC7I6PFOXa/HY7lJhcOEhkzKKib2lZuGREKOJXOlwICJlHKZDopCyXRvE4t1B3dS3dkCwh7g1n7wLvt3PI6lFWXtIwAtZaKlTAxv4VaJYhh4Uinb0T/6rUAIXvn0p7jljbcyUVttyxrZf98Objh4iJVHj2d8DoplsfbwEdYcOcJbH/0wHY2NAJT29zue08mqAYiOqQAw00RLSjAVJcsPBLZSSwQLz1VxcaasN05pf9x+lgGPblHTFqZ7cSnJ4PytY+Yqkhmkt9tgoG/EJzI0YBIJmSxq9DHYbxANmwhFUFGpTltOhhhHF02kbp+esuhoTRFPSAR2Vn3DQm/G2e7zCzQPGA7GT0mpMqlijlPDPl9D0zmqu1pQM2n9Joqhs2X36xzc8WHnPa3CrCdV17nt9TdYdvI0AogHg7z30AOZ0iEAKb+fPY8/yp7HH82amtj34AN0LVzInS+/momGGrY87nnuBZ752u9iqSqx0hJKBwavKIslBLHiYrqmOcP+SpzfuIEbDh5idGSGhd23Zb6FYl91WDJLiQyjSCjvjdG1ZP52oHQVyQxhGnZEU85yE0KDBvXT1GlwLIGAYiuTMTNPQlCwspJS0nwpyfAMi8QOBmi5nGTZKj+aJhBCsHSZn6ZLiSxlUlQsHH0tM02kzEd5b4wFl8/ktusFgtEQ3liYVDD7DV4Kge4rzBrZ9quXWHThYibnozgcZsdzz3P4rjtYffQYJYNDxIuLObztTi5suDFnfnv5yVOO/UyElNS2ttG5dAmH77ozS9kA6B6NcxtuZNHFywTDYQTQvWABu558bNbn0MMV5bz94Se5+1cvISw7UTRWXMKbH/vItFYYvh5RzfzTxVqeKt7zBVeRzBDJZP6HIjRkUls/M+cVQrBgkdcuRT+8UEJFpUpRcWEDZjRi4fRMS2krwcpq28TWPIIVqwOkkia6AYGAQJnCYJK49+fw+O9Nat9IuZfF5y7gSzg3VrKEQAqJJew3PIntkO9rKC5oMA5EIllKZBjFMLhp5+5Mo6eicJjbXnsDxTQ5t3lT9kHynEdYVua7unzDOjTDYOvO3fgSCXSPh6N33MbJW25m//0QiEQxNZXUHObPtK1Yzo+/9rtUdPdgahpDVZVXjVN4PmOqzr8dCei++T1Uz2/prmLG8yGYhv3WP5GcESkl0bBFImHh9QqKS1XH6aNkws5TsXeyf9++gKCqtvD5VV2XOLUhlBJSDlFnXp+KN09F905fFYcrbmDIU0xdopetA6coMyJ5z73pQ4N88MuJRf54Egke/dHTFA2F0HTd0Z+Q8vu5sHEpRUNJAjEdQ1OIVPgL/oEWhcNYqpoTsaBAjkPKYxhs2b2Hc5s2Zg2w529cT31zS46zWjMMlp06TdfSJfZ2GzdwfsONaLqO4fFkHWNsFNVcIRWF/vq6uRbj2kIRhKoClPZlT29JAYM18yjx1gFXkcwQXt/0mfmmaU816bpEWva4onTpLF3my3HQt7WkshILpYRkQjLYP2JJXIl8metCgWCw8Ou6FFzIm3W3YwgVhCDkKeZS8WI+2vo6FXqo4ONciZvf3klp/0CWA3hYmRiqapc9f+IxpKoQqQwQqZz4j3KoosK5cCTOTnBfPIFqGFmlSZpXr6Lj+AkWX7iYk6C48vgJzm3aSF9D2lQVYkKVf12uDYaqApiKoKwvjmpKUj6VgdoiUoH562gHV5HMKD6/IOlQ88rjEROyRnq6dNsSSB9KStuq6WzTWbxsxBTQU1am4+FopLQd/YUqkkBAIRBUiMeskZdtYVtZxQ4JjU5IYHfNVgxl5BGTQkEH9lVt4JHOPQUdpxAaT5/JiSJKp4pw7I7bOLdhw5Tf5HW/n1M3bWXtocMZ/8XwGZ2+yZTfjzm2Eq8QREqdHaaKZbHs+IkRRTLNBEMhNrz3Pg1NzURLijl++62ZSDGXeYQQk37ZmUtcRTKD1NZ7strmgm1N1DZM7O0iHDIdp5piMQvLkpkprvFijyZa/HvREi/9fQaDAyZISUmZSlWNp+BorITqI6k4zHcJhU5/Td79vnlnAzt+Gc+73gmnbHKwHenHbr8t4wSubu9g1dFjaKkUTWtW07Jq5YQcxIfuuZtwRTk3vr8fXyxO5+JFdDQu5eYxuR+6pnH4rjsc/Qbjlb2v7egoWJaJUBQK8eS/fA9NT6FakrKBAWrbO3j//nvt6TcXlyniKpIZJFiksrjRR2+3TjJp4fUqVNdqBItmpvCdxyPQPCIne14IKCuf2DmFkt3/fcKyWM5JkQABM5l33bsb/m7CDvfmVStzrBJLCDqWLskoihve38+W3e+imCaKlCy+cJGuRQt58+MfLVyZCMG5TRtzBt9EMMhN7+ykeChEvKiII3fdkXeAlkLkbQg2U3kYG/a+hyeVygQEQLq/yFvvcOHG9bbvx8VlCriKZIYJBO3+IlOhpFRlaDDXKgkGs/M1hiO2Wi4nM02qhAI+n6CiavyvOpm06OnUiUUtFBUqKjUqq3MrBReKJi1Whi9zvmQp5qjpLc0y2Dx4alLHzMf++3ZQ29aGPxbHo+voHg+618Pehx8C7MZRW3btyYq48ug6da1tLLpwgZZVq6Z0/qa1a2hau+aKJS0aLl+mdHAwr1/l1M1bCzqfsCzWHTjE2sNH0HSd1hXLOXz3XcSLnafvGpqas5RI5jhSUjIwOKUCj1cbwpJIwfyPMpOSYDhFIJLCUhUi5b55Hbk1fyVzyVBT5yEes0ac7YqdXFi/MNda8AcUlq/2Ex4yMQxJIKgQLFLGVQi6btF8MZlx0psG9PUYpFKShoWTd/hu6zuEoWhcLlqEIi0sIdg0eJrV4cuTPqYTyWCQX/zWl1hy9hwVPb0MVVbQtGZ1xtHd0NSMpSo5EVceXWfpmfNTViQZxrnHwrK4+4WXcjPC0//31tUV7LPY9quXWHzufMZXs/zECRZevMQvvvxFdH9uH5tYcTGlg0M5yxXLIhG8uubiJ4snYVDVGcGbsJ+BWLGH/oZi+7mYb0hJXVMoU/JHAsWDCfrqi4iVTb5P0UziKpI5Jh4z6e7USSYkqgqV1RrlldmWgKoKFi72EA5bWKbE51coLnEO/x3efiKZ8gO9Rk4JeSkhPGRSUysdS88XgiYtHuh+j7jiI6YFKNUjeKQ9+Bm6pLtLJxIyMyViauo8E2onPBpLVbm8bi2X1+Wu071enGwASwhSvtmJjCrr70dzqFElgFgwyItf+GxBxykZGGTJ2XNZ1pVqSbzJJKuOHufkrTfn7HP8tlup6noejz7ixzFUlfbGRpLXQVkTxbCobx5CWCNPQTCiozWH6Gwsm3fWSfFQMqNEwJZZSKjqjBIv8SFnvWrElXEVyRwgpUTXJXpS0tYy4ow3DOjpMjBNqE7nfZimpK05RSI+UkOrslogSqdPnnieAoxC2FNe2hSr4wasJIHUiF/EsiRNFxMjmfMShgZNEnGLpct9/Kdf/Xf+bJKJiU60Ny51rMprqSrnN96Ytayqo5Nb33iT6o5OUj4fp7du4eidt085a9vQPHmDAmKlJQUPZpXd3Y75LJph0Hj6DJquE64op2n1qkzp97YVyzm0/W627tyNFALFNOloXMruJx6d0jVdLRQPJuycqlHLBOBJmXgTxrwLrQ0O140biwBf3CBRNL/kBVeRzDrRiElHWwrLdC6sKCX09xpUVmsoiqC9NUU8ZmXWgb3e51MoKRsZ4C1LEgmbJBMWPp+SN2HRCZ9PIRF3yJGQ4PVO/9tPOGTmViKWdhmWWNQqOAO/UCxN4/VPfIwHfvLzzGCumCYHdmynv24kqa60v5+Hn34mkzDoTyS48f39BMNh9j768JRkiJSXEaoop7y3L8tfoXs8nN6yufDjlJY6KiSJrWSqOzsxPB5ufusdXvzcZ4iW2W8cp2/aytlNGynrHyAeDJIoLso5xrWKN2k6D8yAJ2WRmoPZPWFJikJJ/NEUpqYSLvdjpEv1WOP8bq15OBMHriKZVZy6Izoi7KkfRYV4NNdakBL6+/SMIjEM+w3fNEknLJqoXTpLlvvxFDAtVVGtERoyc8KUg0XKtFQkHksybjkrUWxlUuTgM/YkDIoHE2iGRbzIQ7TMPyETv3fBAp752u/S0NSMput0LFmcU2bkxn37UcfUwtIMg+UnT3F4+90kiqY2DfTWRz/Mw089gzeZREiJkJLLa1dz4cb14+7nTSRY9cExatraGKqsJFJWmpOACWQ+e3Qd1TC48+VXeO1Tn8istzSNgdr8odfXKsmARiCSclQmqQLrrE0nwpTUNw2h6WbaB6JTPJigd0EJ8RIvkXI/gaiend2OrWBS/vk5ZM9Pqa5RBvN0R8xB2nWsnJILhxldhr67Q88qnGj3A4Gu9hSLll45YsznU1i01EtXh04qKRECSsvUCee7FIrXryBEbvMtIewqw2MJDiWo6owi0tMT/qhOyUCSzsayCSkTS1VpW74s7/rKrm7H6CZLVSkZHJi8IpES1TCIlJXx89/5LeqbmwlEovQsXEC4omLcXYOhEE987wd4UjqaYWCol5FC0NtQT3VHJ6SnqsbeBUVK6ltaUAwjM8V1vRIp81HWF0eaMnOfLAHJgMduejbdSEnxQIKSoSTCkkRLfYSqAplntWQgnlEiMMoH0hGhtbiCRLGXUGWA0v54ZgMpBN2LSuedP2eY6/sJm0aiEbvviGFIiooUKqs9OU5qpzpVYxHCbmurKAKP147Qkg6FP4PFI5ZCJOxcGTQasQqu6RUsUlm2UsWybEUydp9UyiIes1BVQVGRMqXuh8OtgMdOb2maoCh9XW//bYAdfxIHS1LVFc16O7ObUpkUD8QJV02Ps1hLmXQtWkpZX19OYUbVNAlPpvOflKw7eIhN776HJ5kkGQhwcPs2LmzcUPAhbnpnF754IqPghmXzJpI8/Qe/j2YYfOSfv4MvmT8353pHqgodjWWUd8cIRnWksJXLYPXMBBpUt0UIREcsoNL+OMFIio60Y78o7GwdKZakpN9+podqgkTKffhjBqYqbL/IPFUi4CqSaWGwX6e7c8TaSCVNQkMmjSv8WcokWKQQizpP64Ad0ltRpVFVY38tQgjq6j10tutZ+6gqk04UvBJj/SpSSro79UzvdgQoAhY3+vD5JzftpaiCJct9dLXbeSsAxSUKdQu8GQUW++NvgPKHeJO5ZdfBViZF4dSUFYmqm9S2hm1Fsng9fXWrWHX0PerbLgJgaBpNq1eRKJq4T2HtwcNs2bU7Ey0ViMW4/fU3MTWNyzc4hJc5sOjiJUcrqbyvj1vefIt9D97PUGUFNR2dWVaJJQSdixfPiDVS39TEpnffo3hoiN76ej7YdieD1dXTfp7pxPSo9C0soW+Gz+NJGFlKBNIvPimTYDhFrNSX1wcigPKeOIZHJV7qw/SoRMuujmTROVUkQohHgG8CKvDPUsq/HbP+i8D/Awz38PyWlPKfZ0s+KSWDAwYDfSZmOiejps6TNYBalqSnK3fKyjShr0enblTfkfIKuzvi6Gmo4WmkugYPOFgCpeUaHq9Cf5+OnpIEh62dUdWFS0pVQkO5VklxSf78EdO0HdvDvpB8jvlw2KIzGcQKCgLREEKCCbQ2p1i+yjfphEWv107UlOkbl+84UhF567tYU+1/ISW1LSE8KSszCJseL2c230kwMoQ/HubMlk0c3nbXpI696d29WSG3YPtctux+t2BFYmgaXgdrQwDLTp2morubir7+jPzDtyoR8PPuFAMEnFh66jTbXnolUxImGI6w8NJlXvrsp69L/8tYfPH8Lz7+mE6s1Ee4wo83EXG2SoCKnhjx0qklMc82c6ZIhBAq8N+AB4FWYL8Q4pdSypNjNv2xlPJrsy4guR0OoxGLWCxJ43JfprqvnpJ561hFxzjKFVWwdLmf/h6dcNiyLZBKlbKK3AxyQ5f09ujEIhaqBpXVHkryFEysrfcQj1sYxkjCoqaKLCU2mqFBw+7rLkZCIhcs9uZES/V7Snlx9Z3EfUWAxJNKsv7A25QO9mKakmRC4g9Mzdy+kiLSvSqGR8ka7MGe4w5XFJ6c5Y3HKR0cJFxWlsmd8CZNNN3K8S9YqsbOJz9O34LJt7FVLAtfIuG4rihceJ/4M5s3suG993Om28AuV1/d1Z0T1moqChfXrydaOo0x4gBSctsbb2XVFVOkBF1n685dvPFrH5ve812FmJoyUjF0FJYAQ7PHjFiJF1/MR+mg83SkpufvZTRfmUuL5FbgvJTyIoAQ4mngw8BYRTInmKbMUiLDSMsOv61PZ3yrav43Zk0TxKKmXb03KfH6BNW1HmobvNQ25D+3YUguX0hkfAi6Dh2tKVI1muOUlqoJlq30EY1YJBMWXp+S1xpJpSy6hqfKRrUdaWtOsWKNP5MQaAiVXy68j6TiyfTvTWoePrjjYW5//af4zGTGmpgJjrykweOAEPQsKqW2OWR3kBO2YzJc4SdeXMD0npTc+vqbrDp6DEtVUUyTy2vX8O4jD6EYlp1fMuY6BKAaU/sxW4pCrLiIokg0Z12oonB/y7Hbb6Oqsyun9Px4qJZFVWdnwecoFF887mgdKUBN+8wUnLzaiBd7sIRAIHO+r0h5+sVHCAbqiwmGkmgOj5nhmacxvuMwlxIvBFpGfW5NLxvLx4UQR4UQPxVCLHY6kBDiK0KIA0KIA4NmalqE01Myr29rdAKf5hEEHHp0CGE7xFubUiTiEsuCRNxOLgyHnM3fYfp7cx3RUtplSyzTefAWQlBcYlfoLSlV877phwZzo6WGGe20v1y0AEsoOU3gpRB0LbQjn/yT9JEUylsf3w2A4VVpX1FO9+JSehuKaV1RwWBtUUHOxxv37WflseNopok3lUIzTRrPnGXrzt2kAppjToYlIF40xYx3ITh4z3aMMT4KQ9M4uOOegg8jVZVdTz6O6VBYMZ8at4RgqMqhfpaULLh0mTtffIk7Xn6V2tbWzCotpVPT2kZpX34vgu715j1n7DrKSxGWJBBO2omDY1uJCkHX0jJ0n4olRiyR7sWlWFr272WwtghrzCNsCRisvvrK1sylReI0Cox9Tp8HnpJSJoUQXwW+C9yXs5OU3wa+DbA2UD7p12RpyYyS8HhF3gF3bJLegsVe2lvsxMHhF9zqWo0hh0FbSujpNCgpzX/rYw65IzCSaR4ITt4BZ1n5b481SnnF1ACmw3uGpWkkA0HqF3qnFLk1YYQgGZx4gMENBw7m9EnXDIM1Rz7g4I7tOR3pLGFPT2TeHqfApfU3YGoaW3btoTgUIlRRwcF77qZ9nBBkJ256e2eO1ZSv8COAqam5BSCl5M6XXqbxzLlMF8llp05xautWoqUl3PzWO0hFQbEshiorefPjHyFWkj21Z2ka5zfeyMpjJ3LK5h+7/TZK+/pZeuYsQlo0r17FYM215zPxR1PUtIYz01cC6K8NEqkYGfwNr0rHsnJU3UTItIXh8NITTT9j5T0xVFNiaoLB6uC8rac1HnOpSFqB0RbGIqB99AZSytGvR/8T+MZMCRONmLS32NaMxP7e/QGFxJjkOSHIaRClqoLFjT50XWIa9hSWogh6upwtD12X44blah7nhliWRaa/SaBIoaLC7jzo9ysF18MqLlEZ7He2SopGhRTXJfpQkIxVaaqps8Y3QIlydUSTOE3FAGi6jpCSoeogKb9GSX8C1bSIlngJV/iRk6z5NZbmNatpXrN6SsdYceIkmkPjLicksPehBwlVVmYtr2lvp/HMuUzWvgAU3eCGAwdAKFmKoaKnh/t/+izP/+YXco6//757UQyT5SdPZcrGHLnrDvzRKE9+9/sIy0JIyYZ9+zlxy80cuXsSgQrzFGFa1LSG7ZeOUb+fiu4YiaAHY0x1XrOA0kLRcr+tUBwqR2spE003MVQFFJFXIc0H5lKR7AdWCSGWYUdl/TrwmdEbCCEapJTDk68fAqa3/ngaQ5c5GecSSMQtSsoUwkMWEtvnUdfgcZzKArsfyOhMck0Dw0GXqOr4TuZAQCEadrZKhseTWMQiFrHsmSdp557U1nuu6LwOBO2Cj5HwiDIRwnb6j24PXJvsoyHeTUegNtPlULUMqvQhluld455jPtHTUE99a1vO8sGqqsxAGC/2Ei+ev21tnVr85sMSwtGZv+j8RceikYppIca8LihSUjowQFlvX06JeUtV2fvowxy4bwf+aIxoaQmBaIyP/PN3sl4cP6gAACAASURBVAICFMNg/f4DXF67+pqxTAIR5x47QkLRUJKh2ikMp6N+t8K0qG0N440bWS8MpiboXVAyKct8ppkzH4mU0gC+BryCrSCekVKeEEL8eyHEh9Kb/aEQ4oQQ4gPgD4EvzoQsTqGzwwSDKivX+lm52s/yVT6KSwp/E6+s0XJeIGyLJv8DJ6UkFil84JDWSCvdoYHxfS/2+QUNizwsWOylpFSltExl0VIvNfXZA6kAHu7czW19H1CZHKAiOcTN/Sd4sv1tlAn3W5wce790lL//+tScxvvvuxfdYztAwR5oDU1j34P3T4eIs0LH0iUZ+YfJ+w0IgeVgLRpeT95waadXD0tV8Mfzd6rUfT7ClRVYmsbi8+cdD6KYJkvOnst7jKsNp3yekXXTd56qjgjeuIFCOus9/U8z7HB1VS98fJgt5jSPREr5IvDimGV/NervPwX+dKblMM08tZ+kHb2lKGJSKre8QsOyoL/HyFiuFdVa3iZTibhFW0tq3NIo+ZASBvpNyiuv/LYy7Ji/klJUkdwYOs+NofMTlmc0hlDp85bjs5KU65EJ7bu1ehkwsda7o+mvr+OFL3yOG/fto7qzi4Hqao7fflsm50HVTUoGEniSJsmgRqTcf8UeFZ6kgTdhonsVu/bRDE83vP/A/Tz2/R+iGgYew8BQVVTTdPSTSEXQ5DCVdmndOjbu3cfYfgFSCAxFyQkvVkyLvtraK8q29PQZ1r9/ANVwKPopQIqrLwIpH/EiD04FbaRg2ixaYVoEo3r+CD0JxYNJhmrmV/l/N7MdKCpWGehzrv0UnEIlWiEEVdUeKqs0TNOe0gI7Igwh8XhEZirKNCUtl5M5fUEmwtiILj1lYaUr+E42cXCqnC5Zxp7qLQgpsYRCuR7mkY5dFJuTVw4TJVRVybuP5ZZM98Z16ppDIzW8Yjql/Qk6Gsuc57elpKY1jD+mZ5ythlela0npjDZICleU8+xvf4mVx45T1dlFf10tTWtW///svXmQZNd15ve7b819qb2qu6s3NPaNAEgRBBdAFLhIJEhKHFGWRmLY45E0CseEQ56wFXKEw+E/xhzbUsRMxChCipmxNbKlGUlDiRD3DSBEgiABEQuxdzd6q33NfXnb9R83M6sy82VVVnVVdVd3fhEdVZ35lptL3XPvOef7Ph54+hmOv30WKQSBriEk/OjDH24p/m5GKZPm2Y8+zvu+8a3WzkRIyQ8+/lEefPoZouUyRiM4eYbBix98P942Xi13//BH3Pvcc12kyyakpocGtcMK39TJD0dJr1YRjT81KaCSsKjF9mYq1YKtGyk0lDzQ9YZBIEHVDWIJjUopaKsbJFP6nrS4CiEwDNU2PHfFwfcaukmm4MgxCzuiUSz0bsvtF01CoVNXO5umd7uuw+RRq80rXkrFbC8XfXRDkMromHvcv75gD/ODkQdaNRaANTPNVyc/yD+a+UbfvIj9wvB8qUvKQvqSzHIllIyYXqkSqbhtxVaz7jM8X2L56B6T/zrgRKO8/p53tz32zKefIFIuc+zceZBw5ZbTW8rDX7jrTmZOn2Lq4iWkpjF34gSeZTJ34ji3/+RFjp17h1o8xusPPcjC8ektx2M4Lvf98Lm2Ij2ot0Wiaik/+cAjFIaHQs8/rCiMxKjFTeJ55RlSTlp7qoNl1r1WkApDILguaySDQIKa6I8csygWfPLrfkM40SCR3LuJ1fclMx07DteRXL5Y5/StEXxP9gwksbjG2KTJ+orXJfeuxq90uobHTKRU19ysDux5qtvr5BklKy+lZOaSaleWjeXP6rLH1DFrRzWg7fBq+gxeJw9F0yiaCdasNMNOt/1rJ5695w9gD02umtD8ANPp3v4JehdVE7laVy68dXwglQjZAaMWj3P2vnv7Pt6NRJS/fMdjP33fw/z0fQ/3fZ3U2lpozUUA1ViMr/76r4XujG4EOFFzX8ywrKrL6Gyx5wIrQLWml69D+ZRBIGlACEEqbZBK789bEhYAQNU2SgWfaExrcVDaxqXB8KiBbWtMHLEYn1IBx3UU895xJbGYRnbIQDeE6sYKSY9JIL/uMTJmUsj7G0Gk8aREsedP3xbp2xBrO5SNaBehEUCTAVU9AmwfSADueyLHy0/uQn13C4Q5Jrae6yWqt8VKUcgtCuBXAREEnHjzLU699jqBpnHu3ru5csst26+ApWTq4iWmz57FNS3O3XN3VwfW1aCSSIR2k0lgbXz8hg0i+4nMSjX0OyYBTxdU0jb5TXL01xMGgeSA4Lk9CvqBkkRJpnWiMa1tghdCtQJvbjcWQiAE2BHRkmlpu0+vnY2kVcTfit1eqwZtKbCrwfHyPMv2EL7W0V8vNEbra3tyj91CaoJqwiRaai9sKg2v8BVfNWESLzhdK0bH1nfEOzEcn+xSmUjZRQpBKdOQNO+cIKTksb/5EhOXr7T4H5OXr/DOHbfz3Mc+ssWLkzz6t08ydfESpusSCMHtL77Ejz/82I52L1uhlogzd/IEUxcuthXqfcPg1fe+Z0/ucbPBrHf7ygBIDZam0y0HxesRN05LxXWOaEwPW5yrYBFTulhHpy1Gxg3siMC2BSPjBkenrR0VyqPRHi2eYsPDZKvL7WVN/s7COWJ+DT3YyLMZgceD669iB+3pIwnkjQRF4+C6UVYnEzhNKQutIY3SMBUKQ240RqCLlqxF87y1yRBLxx7QvICJi3miJVVr0QNJcr3G6Gw392Pi8pW2IALK/fD0a6+TWVnpeY9j5863ggiotlXD83jPt7+LtUVL707x95/4ea7cchpf13ENg1o0wg8+9hEWjx3ds3vcTHAieviuVoJ/netvDXYkB4R4QsO2FWO9bccR04g0Jn+hCYaGTYaGd59/tSPhhEPTEiQb9Y901qBS7rb8bbL59wqW9PilmW/yauoMF+NHiAZ17sm9zbFqOzdk0R7m2+MPU9NtJJByS3xk8VkyrppcP39rjd/ds1FtINA1Fk6klQqw4+NEDDyr96rPN3VmT2VI5OvYVQ/X1illIkrxtU8kcjVls7vpsabEuFH32tjRUxcuhpIIdd/n/V/+Gt/83Ge77IIBjr/1dlvw2Xi9OpOXLnfVSHYLz7J45lOfxKzXsas1yqlki+Q5wM6RH4kRKefb0luBgMLQ9ZnO2ozBp35AEELJqAyPGli2UErA4wZHj6v0lOsEuCHy0VJKAl/uSGl38qjJ6ITa2ViWYGjE4PhJu6WNlUhqpNJ6wwlRlTE0DY5M795fpBfswOXB3Ov80uy3+Pn5Z7qCSFWz+crUhyiZcTzNwNcM1q0UX5r62ZbWV+2xL+7pmNoglA92JWVvGUSakLpGcSjKypEk+ZHYjoIIgF3zwslrQsnab0Y9GgkVaxQoGZOP/sVfdhfVUOmlXl3k/j4YXbm2MmsamZ/H7CGdf7NC8wJED6HVTjgRg6VjKeqNnYlnCHKjMfKHQMRxsCM5QGiaYHjUbJOCr1UD5mY2SIimJZg6ZmFZguVFt6WLZZhKnqWfriohBNkhk2wPcqIQqr6SHVEyK7oOiZS+Z0X2neBs8jhdjiBCwxc6l+JTnCrPhJ94SJDI5Tn1+uuY9Tozp09TiwwRwe1ewUnlvbIZF+68g/t/8MPQ62pSksznGb8yw+J0uyj2uXvu5tTrr6N1kASFlMydOH61L6kNhuPwwSe/zOSlywSGjub5vP7QA7z4wQ9ct7pQbZCSWNEhVqwjNY1S2t6T9lqr4jI6V0RvtPrXYgYrU0kCXRAtudgVF98QlNORNlXgesxk4cTeNpYcBAaB5BoijITo1CVXLtSJJxsaX43FjOdK5q44HD1u7Vkx3LY1bPvgN6USxXY3pE/RiHUV40FJmVT0638lthVOvPEmj3ztG0rIMAi47aVXuHTmVi7f+m5lQNY4LhBqNepG2t+HSjLJ05/6JI/9zZfQw5iqUpJaW+8KJKvjY0hEG7FNoshzmh8Q7OFf/cNf/yaTly6rgnuj6H7HT16kMDTE+Xvu3rsb7QekZGymiN3gBkkgVqiTH45SuAo/d93xmbhcaFseRSoeExfz+DpYToAm1eeeWamqXch1yA3ZCQaprWuIXi3BQQCFXHeXV9OT5DDjjeRJ/uz4p/i/T/4if3ri07iagRF05/MFMF7bKCh/Nfg3/d9ESqJFh9RqlWjRCU3/7AkC2fPaRt3hkYYlrR4EaKhC+fGzbwMFnIjRmtwrSYulHoTG2dOneP7RD+GFpLgQgtxod0tvk+2+eSITqBblE2+9tdNX2ROG43D87LkueRXT9bj7R8/v2X32C82dQTPVKFD1qsxqFe0qjM2yi91mZkorK8CqB637aVL9G5kt7t939IAw2JFcQ/RsCW4uJUOec5z9+cIFgSoA76fHyNnENM9uYrrXdZvziePKbRHR2pkYgcdUdZFRZ711bssxcRtoXsDEpTy6HyAC1Trp6xoLx9NdxkK7RaTsMrRQwnADpIBixu4y2pq8fDmUsGe6LiffeJVnPvVJ2rohtsD5e+7m3h/9GK1SaQkHerpOKZVS5mMdEuTxYrGLcQ5KOj+eL+zmJYfCrDs9+Ti9bIavJ8SK9dB6lQSiZZdyenfEP7tDtXczwr6BWiAx637XjvQw4fCO/AaAagnuJhCGERObiET2dqKv1wIW5pSLI6hC/PiUhWHsfUB5fuieNrkUAE8z0KXPu9Zf51zyBEIG3FE4z12F87u6x9Biuc2HXQSK1Hfk/DrllE1+dOcF8s2wah6jM4WNVayEZK6O7ss2WZUgbAfBhnyIOrm/99izLb7yG7/Gu7/zFEffuaBSVlISLxT46H/+K1zL4ru/+GlWJycAWJmYwDcMtI7OLc80WZ2cIFoq4Zkmrn11DOlqIo5j211BKxCC+elQM9PrCoGuhetaCUFwFQuqQIee3Q49sBVB9jBgy0AihEgBo1LK8x2P3yulfGVfR3YTIJ7QsCyBUw9rCRZdQpJCwMjY3uVSPU9y+UJ7jaZUDHAu1jlxeu87uMpGeM2jrlncn3uTB3NXaTfTKJx2jrqZ1knk68RKDnOnMrsWWUytVLrYx5qEeNFh3Qtau55eE6lnmpzbRe2gkkzyvU8/QbRU4jN/8u/bahKm6/KRv/wr/uqf/TaeZbIwfYy10VGGlxYxGgV3T9epJOK859vfIVquIJDMHz/O93/h49RDWoj7ghD88KOP86Env4zmKdlzX9PwTJMXP/j+3V3zAFFK24127PbHJUrpd7coDMcYXiiHy/PTviuRKNkTzzrcVYaeoxdC/DLwJvBfGp4gmxXj/p/9HtjNACEE0ydthkcMTEu16o6MKRLiyJjJ2IShFII1FVymT9rYe+iTns95oTsf15VUK1chQ9wD6R4S8nG/Sg8qVht2VCcJgUD5bSfWd592MZ0e7GOhcuBNBIbBU5/5FK5p4pomnmHgGQZv3X/ftoKIW+Hk62+E+swTSKbPNrw/hOBbn/ssr/7MeyimUpRSSc7dczexQpFkoYjh++h+wOTFS/zcX/71VeXnZ245zdf/q89x+bZbWR0b46377+PJ//o3KGWu/84jN2KwPhZreasHGviaYOlY8qp008ppm0rCbAlYSlQAWTiWpJqwNu4nINAEy0eTh6PDbQtstSP5feBBKeW8EOI9wJ8JIX5fSvlFeqscD7BDaJpgeMxkOGSnkRky+/IX2S0274TaIFUtJtZbSHZXeO/qy3xz/H1tXVpG4PEzqy/vzQ2EoJIwiZV6+zk0yX89KwWBJJGvES84SE1QzESoJjbUXZ2Igel073qQ4HawjxeOT/NXv/NbHDt7DtNxmDt5gmI2zNGif0QqVfQQjSstCLCrGwHSN01efuR9vPzI+wB46DtPdRkz6UFAem2docUl1ibGdz2m1ckJvvepT+76/GuJUjZKJWVjV5RczZ4o+QrBytEUZs0jUnEJdI1K0kJqgpW41XrcNzQqCeuaiH3uNbYKJHrT5lZK+WMhxGPAl4UQR9kffboBDhiRqKCYD1+Q7oV8fiemK/N8ZPEH/GjoXvJmkqRX5t1rP+VUudsKtwmJ8jR5JXMbf37eYjheJD8S60keXJ9IYF/MKyIYIcZPKA8RpMSq+4hAUo8Y6o9ZSsYvF7DqG6RBu+JSytisjysZlPxwTKXPOtjHxUwEGZIuc22bd+6+q+/3aDssHJ/m9hdf6mauC8HCdG9pkvTaWmgLsRSCRKFwVYHksCPQNarJvVfUdUNaurd6/DBjq1dTFEKcbtZHGjuTR4G/BfbuL2OAfUEQSHxPYhiiZydWOm2wtuy1+co3ZVL2UiplM6YrC0xX+rfPfW7oXl5Pn1FFeh/iBYdoyWX+ZCZUf8g3NGZPZYiVHLKLZXS/XY5ECqjETY6cz6H5QWv1uTIRR0BbEAG1g0nk6hSzUTxLx7N1Fo6nyS6Vsasega5RGIpQzEZ2/mZIiVXziBUdAk30xa6fO3Gc5akpRudmW4ZSrmly+cwtrG/haLgwfYyJKzNdhXHN91kdv3mDyAB7g60CyT8DNCHEnVLK1wGklEUhxMeAXzmQ0Q2wY0gpWVpwya+r9IcQSoZ+aKQ7RabpguOnIiwtupSLyoclldH3tKB/NahpFq+lb8Xf5EEuUO2SyfWqarkNQ2NSrsVNRuZKRCpuo1tKY3U8xshCGa0ZYBrbsZH5EtWY2dN72666rUnejRgsTaev7sVJyfB8mVix3trdpFerrE7EqaS3CEpC8O3PfobTr73O6VdfI9B0zt17NxfuuH3L2529717ufOEniMBHD9QNXcPg4u23DiTfB7hq9AwkUsqXAYQQrwoh/gz4P4BI4+dDwJ8dyAgH2BFWFlUQaaarpISVJQ9dF6Sz3R+3YQqmju6N3/ReY81Ko0sfn/ZVetMWdzsEusbSsRSaHyACiW9oRMpul2giqK4u3Q96tIOy51a6kYrbxWMQEoYXylQTVmiarAmp65y79x7yw8OceONNRubmKaXTLB+Z6nmOE4nw5c//Y+7//rMcPX8ez7J444F38eYD79rLl3VdQvMDYgUH3fOpx0xqsb1zNNxLGI7fsG/WrsvxbYV+EnU/A/wr4FkgCfx/wCP7OagB1M6iXArwPEk0tiFl0kxZ6Ybo0saSUrK+1s2WlxJWV7zQQHI9I+FV8EO09yXdulRbIdA1mrFI98MdqAQqLSaF31b/UOxzcVXtoGGIF5xwoyyhyHCVbVzwHnj6Ge74yYtongdCcOsrP+WNB97FTx79YM9zqokEP9zKx+QGhFV1Gb9SANkwH1ur4UQMFo+l9r/ILSV21cOs+3im1rOQbzg+o7NFFUiAQBesTCUPlWxKPzOLC1SBKGpHckHKMA++AfYKTj3g8sU6MtgohCdSGqaluCXNiTA7pDMybrb4HkEQXjgHxRk5bEh5ZSZqKyxERtvSW7Ihrb1jSIlZd0Mn8EBAJWVTTtmMLJRbxwe6xtI+tGf2/DSken2diJQcMssVDDfArua54ycvbtQ7pETzPO74yYu8c/ed5EZG9nSs/cCuVpm6cBEpBLOnTl412XFPICWjsyW0TbOVkIpUmszVKO7mO9QnRCAZazRuNOEbGovH0+2EWCkZv5Rvq+VpnmTsSoG5U9nr3oekiX4CyfPAl4B3A8PAHwshPiul/Oy+juwmxuwVp81zHaCY747d62s+QhOtmoamgW7QdS7sTxfWQeAjCz/ge2Pv5mL8CEJCJKjzm//rMf77v975tYbnS6GExUCAa+tUkhYIwZWEhV3zkJrAsfV9STOU0zbxQj00qNXi7anGWL7G8EK5lQabunwx1OZWBAFHz50/8EBy+qev8t5vfVvJtaCUiZ/5xM9z5dYzBzqOTpiOrxoqOqBJiOfruwokuuuTXqm22ncLw1Gqie7UcHql0tW4IdyA4fkSS8c2alLRsosWkmoFiOdrVyUeeZDoJ5D8EynlC43fF4BPCSF+fR/HdFPDcQLcPvW0pIT1VY/hUaNhwSsYmzBZmHW7GPGj44dnm7wZlvR4fPGHOMLA1Qxifo37H/of4K935vSnuz6xotNVTJdALWqwfDS1ETA0cVVphUjJIbtUxnQCfF2QH45SykbaAlI9ZlLMRkh2kCOXjyTbTYykJLtcbRt3oOlKUqNj+ymF2Be/ka2QyOV577e+02DQbwS3D375q/z1b/9T6rFrNxFu+Ve0i7WB7vpMXsijNXTpTDfAmi2yPhqj1BGUEvluHS+B0mkTgWx9xroXhA5Uk2CE+BNdr9j2W7cpiGx+bFBo3yfsNGnYSQ1IpQ10XbCy5OK6EjuiMTpm7ls770HBkh5W2Far3/PrvkoZhfxxm47P1MUcSCgnLQrDsR15sG9GpOwyOltsTSKGL8kuVxBSUhxun1RzY3FKmQjRkiI/VpJWV1FfyMZkswlLUyc4+cZPum8u4NJtt4aOS3ddJq7MIFGtwMEeBZwTb76JCOOnANNvn+Ps/XvjEb8beJaOb2gIt93xJhBKHmWnSK1WW0GkCU1CdrlCKRNpr7n0mUmuR8M/h0CgaiqHBIer+nodI/AlK8suhZxalSXTqo1W3+GEZNkCTQ9PT4XBtESXJlY8oRNP7I1nyfWIZ+/5A+7741/l5Sf7k+EQfoDh+IgwSw/A8JruHZBarxEru8yfSO8qpZVernStRJU0eSMn33FNz9K3TLFIoRSMN4/dicZ56/5HuO2lH7QCj5CSH3zsI1SSya5rHDn/Dh/6uy+zMQVKvvfEJ5k7dbKv16S7LoGmIUOEKA3XDQ0kouETf9WQkqPn3+H4W2/jWSZn77mnf/KkECwfSTJ+uaA69Rr1p1rMVBP/DhEt91BMEALTaVfvrSRMEoX2NKoEHFtv23G6tkE1YREtbeyWA6G+F5Xk9dlNGYZBINkDSCm5fLHeJjmSW/eplIMdix8KIchmDVb68B0RAsYmDs+q5VqgWV9AbCjzh4k6NqFJ1UUTKzrbdk6FwXS6axeAKoj7kmCnqspCUBiKqtXwpgC1cOwUZ+8+w9DqHAAzp06G+rdHymUe/dLfdU3qj/3tk9umnrJLy7zv699gaHEJKQSXz9zCcx99HCeyMQlfueUW7nr+H1T3WNu41ZiuClLy2N98iclLlzFdl0AIbvnpa/zkA+/njXc/2Ncl3IjB7C1ZYkUH3QuoxQyciLGrRYJn6phh6SYpuxSlexFLvZDi+cpUgkSuRjJXBykpp+zQRcf1jEEg2QNUygGO06FbJcF1JKViQDLV/+5ABpK11fAgkhnSceqSej3AsjRGxow9c0s8CJT1KCUjRsYtkDOT5M0UWSff5juylzAcf6NI3dHSC+DrQrUDd0CTylNiN4HEs3T0WsjnJwTBLtNl+eEoSEitqbqQFILcSJTSUJTcxNa7shNv9jayOvHW27z1rvtDn4uUy3zsz//Thq6YlEyfPUcql+PLv/GPW5Pc6uQE5+6+i9OvvY7uuiAEvq7z+kMPUhy6Ol2xo+ffaQURUEV8zfN48Jm/58Kdd1CL91d/kZrYtbfIZhSGI9hVt71e1UhBdXrdJPP10AVLrOQSKTnUNhfohaCUjVLKHl5H0EEg2QPUqkFobUNK5feRSGrUaxJNB2sbueharXdytVYNOH5qF1Ic1xiu0Pn2+MPMRifQZICrGQgZoBMAgtH6Gh+ffwZT9ljN7xKxHl1RUsD6WAzf0BmZK3YdE4jwlaM6WRItueheQD3arZmUG421+ZU0r5cbiux+hSkE+dEY+ZGo2tXoou9rmY7To8PLx6zXe5535uVX0Px2pWM9CEitrTMyP8/K1Ab58UePf5iLt9/GyTffJBAa79x1R9vzu8X02293a4qhjMomL13iwp13XPU9doJa3GJtPM7QUgUanVa1uMnKZHc6UQtZoIAKJqOzRVaOJEO7vQ4rBoFkD2BaSuq9y6BKA88LOPdmTa2CpaqBHJm2MHtMVE3DuzB0EhAPC743+m5moxP4mt5iqUuh4zV+X7KHeHr03fiaTs5MMVpf44H1N8i6vd38Pvdbf87Lv/A7W95XC7aqeAqqCZNAE4gOPS4ElEN2I4bjM3Epj9h03VrcZPnIBs+kFjdZOZIk2zDYCnRBrtm1dbUQYsepsbkTJ7j3hz/qSj1JTWfuxIme52VXVrssdEHt5lLrufZAIQSL08e6vOOvFp5pEQjRpVoMAs/sPXXprq9slstbt+juBuVMhHLaxnB8Al3r6bpZixo9ayqaVHa8N1IgOdytPNcJEkmdEFdVBMp7PQhokQvrNcmViw6yR7SwbRHqTigEZIYOX9x3hcGFxNE2QmEnfM3gncQ0l2JT5K0U5xPTfPHo4yxbV5caqSasUHIf0GIZLx5P49h6yx/CNTUWj4Xb8o7OFtF82fLa1qTq0ur0N6kmLOZOZ7l8+zAzZ4ZUa+g1ynevTk5w4fZbcc2NWpprmrxzx+1bFq2XJydwQzq7NClZHx3dl7F24tw9d/d0muwVBHU3YPJCnmSujukGRKoeI7NFkqs7axffEkLg2caW1s3NQnmvpcxhau3tB4dvZroOoWmC4ydt5mfdliFUJCowTEGp0P2F8TxJrSqJxsIChtqxXLlYR8qN3Uk6q5NIHr6472iGSh1tN4+KDdF3KTQ8ofHDkft4Yu7pXd+7HjWoJK0Wf0TJnUAxG2kVQz1LZ+FkptHP3yiahkz6uuurzq+OxzWp8uGdPILrCc9+/GNcvvVWTr/6GgjBubvvYnabQvi5e+7mnh89j+77Gz7xhs7i0SOsj/UXSI6cf4eHnvoeqfV1qvE4Lz/yMGfvvafvoLo2Mc4/fPADPPi9Zxrdaapj4ju/+Bl8M7zJpFeLbmalQikbaefo7BN0N2BoMdwhsQl/l/Wy6xWDQLJHMC3lYBj4EgnoumDmUo8ctIS1VZdhzQxlnNsRjdO3RSiXAnxfaW1tV1u5XhHza9iBQ0XbYqKVMnRyWbaHt7z2fU/ktm4BFoLVyQTllEu8UEcKVXQNIxtu5+MeqovVeu46l58RgplbTjNzy+m+T/VFpgAAIABJREFUT3EjEb78G7/GQ09/j6PnL+AbBm/few8vP/JwX+dPXbjY1i0WL5V493eeQvc83nzwgb7H8eZDD3DhztuZungJzzSZPXliSw5MpNKrRVd11Dn77AOiuz4js911t80IBORHrt+Fx24wCCR7DG3TSiOW0KiUg1ARxVIhoFyskxnSGZvozpUKIUgkD09HVi8I4P3LL/Dd8YfxhNZeBBICPfDwRfjrtP3exWDor06CENQSVnuXzC7gmRqBrqF1kAMDAaVddHcdBlRSKZ55YnfOh+965vtdLcem53H/D55VisM7SPXVY7G+C+u+qUFYC7bc/12AXXEZu1JAyPANeHNHnBuJtfNYpCRWdIgV6khNUMpEDpVgIwwCyb4ikzHIrfl4brilrZSQW/NJpgKiscO54+gHJytzfHLuKV7K3E7eTDJaWyXq1ymZMUbr6+SNOG+lTnVZ8N6X6926euAQgpWpBGNXVAOAJjeIY/sp/ndYkVoPb+k2HBezXseN7E/3YX4oil3paNEF6lET3+y9MNNdn+R6DbOudi3FbGTLGkgXpGR4vtTTzwZUIFk4nsKNbAoSUgk02lWvlX6NFR3yw9FDo7MF1ziQNEyy/jVK5PvfSSm/0PG8DfxH4EFgFficlPLiQY9zt1DGUTbrqx65dS+UrS4lFAse0diN08ERhrH6Gh9ZfDb0OR+BrxmcSxxHkwGBENyVP8vdhbMHPMoQNImEDf2t2dNZEvkauhtQj5ktoccB2lHMpBleWu563DNNPKuP7/qmXetOUI+bqkV3sdxKL6nOud6BK55rkFbZ0MNKrlVZOJnZ1rGyCd0LuqRsNiMQUElY7UEEiJacVhBp3l9IyKxWKWci26Zcrxdcs0AihNCBfws8DswAzwshnmy6MTbwT4B1KeUtQohfQfmifO7gR7t76LpS5zVNweKCu2MtrZsBOpJHl5/nvasvUzZiJN0SluxPXuPpL0R59Pf2sCNnE6JFh6HFcsvwqpyyWRuPUxg+PCvFa4UXP/D+Lka9axq88vDPIDtaHDUvQAsknqlhuAFDC+WWcVklYbI2kdjR7mDz5C9QHjTjM0WWjqW6UkZWzWN4ob0wrqHi2NBiuU2pdytITfQsrgco3lKYLEuYkCionUmk7O4JkfIgcC3D3XuAc1LKd6SUDvCfgE91HPMp4E8bv/818GGxE72R6wiJpB5uqCSU0OIAEAkchp1czyCyEBnhmZEH+d7IQ8xGx5Ao3a39gFV1GZkrYngBotHqGy/UGVkobXme7voMzxY5+vYaR86tq7bT670Yvw+YPX2KZz7x8xQyaSRQjcX4hw9+gNff/VDrGM0LGLtc4Oj5dSYv5Dh6do3Ji7lWwbzJBJ+4nN/Re5hdVGoGzYlCsMHd6ER6uRJ6jebOpF8EukYtanT9iQcCcmMxxVoPmboCXevZIhwcIt7YtZzBjgBXNv1/BuXGGHqMlNITQuRRnigrmw8SQvwm8JsA4+bV5auDRuug2OMPUTcE41Mmi3Pqy9nsiB0aMQ69Mu9B4Lmhe3ktfUYV7BGcSx7nTPEiH1z5h325X3ql2tV5o8nGCtILQlfImhe0yYwTSDINX4rVqW72842OK7eeUZ4kPbryxmYKWDW/FTSQ3VpoApU2ipTdvhsmrHq4QoJV97vGYtW7W7qbCHY4BaxMJRm/nFcckYbMfyVhUdyCjFpK2yRyta7v2n64cu4nrmUg6dXYsNNjkFL+CfAnALdHM7ta/tVrAQtzDrWqOj2R1BifskLJgbtFOmMQj+sUCz5SShJJHcseBJHtkDOTvJo+01aM94TB2eQJ7ii+sy/3NEM4I6C6bvQegSS5Xuvyg9ckxIsOOdffsth7QyMkiJh1ZUG7lYBmC1J9HrWw564Srq2je0HXfSVQyuwsrRQYGvMnM9hVD90LcCLGtjUWN2K0ajrNQUgES8eS+28FvIe4lrPYDLBZU+EoMNfrGCGEAaSBtb0eiO9JLl+ot4IIQKkYNEiBe5uWMExBdthgaMQcBJE+cTk2SZiHnCc0LsameOqXvr/n96yHpCkAkL2VXTsF/VqnCDB7rJJvBmh+gFX12twK9eaqvU84dn9r3jBHxCYk3d4uuZFol/qBBDxDkBuNd11D+AHRYp1oyYEwCR6hmjIqKbvvQn05E2Hmliwrk0mWjySZOZPFiR6e3Qhc2x3J88AZIcRJYBb4FeBXO455Evg88EPgs8B35V7P7EA+54WmYF1XUq0Eh0ph90aEIX00JJ1ThCZlQ+hx7z+f/EiMWMmBYGOVHAjlFd+LHe1aOpGK1x3yJIfGe3tPISXZxTLJfB0pVDdSKWWzNhHHiRihRM7mI633HPW+1mP9TVWdjpObIaDLOMyJmiwfVdpophMo5YO0TW483hXo4rkaQ4tl9VoaV1w6mtwTzofUNaqHyH+kE9fs2y2l9ID/DvgG8Abwl1LK14QQ/5sQ4onGYf8eGBZCnAN+F/i9/RhLvR7O80CC06ft7QD7h5OlmdDdgUByunR5X+7pWToLx9NUEya+JnBNjbXx+JaM5OJQ9+o2AJyIgdvnivpGQmqtSiKvFJi1QAWSeKFOZrlCYGgUMnZbHUICvqY6tQIBgQbljM3idKrv3Uu06PTMh9diRugioBa3mD+V5fJtQ1y5bZjcWJx4wWFovkRqpYLmBRh1n6FGEV8P1OvRAsnYTKFNxPNmxTX9dkspvwp8teOx/2XT7zXgH+33OCJRQbFHY4g9SD9dc0SDOh9e/CHfHX+4tYoNhOBDy8+T9Cr88L95hfv++O6+HRM7YTg+8VwN3ZfU4hvcENdueLn3Cc/SWTqWYni+1Ci4KgHH1YnuFMnNgNRaLdQtMrlWwzM0TMenHjXQvQAtUAEkPxLrqj8JX5JarRArOgS6RiEb6Vl49w0N2aOAvj62zecgBMIPmLyUR3eDFuk0vVqlnLR6yp5ES7szQbuRcPMtk0KQThusLXu0KToIiEQ1ItHDU/C6kXGyMsevX/wSV2ITSCE4VlnADjbaM//1+yZ59Mmd80mihToj86WWrEW8UCe5buxoFbwZ9ZjJ3KkMWiCRQhyISGA/SORyPPj03zN5+TKObfHGgw/wxoMP7CuZcitPjmzDkrgpG7I6mcCJGEoPS6hUD4AIJJOXcq2JHXzsikthOEo+hPldHIqq9uEOIzPH1ru8Y8KQXq1uuhetn7GiE36C3M6u4ObAIJDQZKBHWFp0KRd9xe3IKM/1vaKtyECSz/sUcj6aBpmsQTypbXn9wJfk8x71msS2BamMsWMP+BsJlvQ4XZ4Jfe7Ze/6AP3zqF/nd/2ui/wsGkpGFdlkLTSqSWiJX6+1YJyXRkkOk4XfRxUC+CjfE/UC0VOITf/r/KpMrKbFrNd71998nvbrGcx99fN/uW48YRMLcIqGLyT0yV1L+9EIgpGxJhMRztbaJvXluarVKMaNkTDQvILtUbk32jq232oqbcGwdEchtA3usEE4QbPq9h+1KDlOb7n5hEEgaMEzB1NH9KXZJKblyyVFOio0vYqXskM7qjE+G39N1Ay69UyfY1Pq+uuwxfco+NErAC/YwPxq+lxU7S9yr8cD6a9xaurRv96s99kUIEXEUfkBmuUK8MdGUUza5kRhW3WPDyX0DinzohAYSEUjGL+cx635b6mPpaIr6Hk0oZt0jnq8jAkk1aVGLmVe1c7jjhZ9guG6bQZTpetzy6mu89Mj7qCX2J/W2Ph5n/HK+tdvrLKR3Qlkiq6PSq1Vc2yBWCp/YEQK75lGNm0xcUtyN5nXt2kaHXPOxeNHBdAssHk9vPegef1oCqMZMIg0dr+ZOqjAU7dnWbdQ9IhWPQBdUEtahaufdKQaB5ABQKgbUau0qwFJCft0nOxyEBoalebdNm0tK8H1YnHM5duL6z8cu2UN8ZepRvAb3I2+Z/P3oQ9Q0m3sLb+/bff/wXyy070qkVBONE7TmiESuhl1xWRuP92RM92IVJ9arrSACGyvrkbkis7dkrzpVlFivkV3a0IlK5OtUExYrU4nua0vJ6Owc02fP4ZkGF+64g8LwUNc1x2Zn0YPutljf0MmsrrCwT4HEiRrMn0iTXq1i1Txc28BwfOyQVugwn5fUWhXP1JGEdcJJfF0QKzpdPJBm0Ork81g1D6vq4UQ3pj3NC0ivVIiVXAJdULd09E3fFRrXciIGy0eTxPN14oU6gSYoDkXDO7akZGihTLxQbw1oCMHidKqv9NphxI35qq4zlEt+T42tSjk8kJRL4ScoWXq5Zym3/cLz2bvxOuThPc3ghaG7uKtwFr2nMMTVoXNXEi05GG77xKA1CG6ar6xwhdfOUgkEobpIAIkeqQ8tkJiOf1XdWZqvUjSbry+keg3RsttuzSolD3/9m5x88y0M1yXQNO7+8Qv8+Gcf5ez997VdNz80xOjcfJdlreYHlFP9NxPsBp5ttLH6o8U6I3Pt6cTOSX/z+IrjcWLFelfNwzc0nIhBtFQJT0X1GI/p+K1AovkBkxdy6E2rZU81Xvi6sl9uwtcFy1PxVnBopt80CcuR7k6wWNEhXqhvjEuCRDI2U2T2dOaGFPk8HDmSQ44ebqEIQe+axyH/rq3a4atzKTSq+v5IiDfx9Bc2UlJWzeuZ87acgKWjKQJdEIhGuqLxXDxXRYSQ23pZ96rnNveySpKrFY6cW+fo2TWG54ro7takxEjZDf3cNQmxQrs3y9Fz5zn1xpuYrtKl0oMAw/N4z3eewq6060e98eCDXZa1vq6zdGSKYvbq7Ix3impDMkQ22nt70QclUI1bOA3md7MdOBCKV7J4TDVDuJYRKmXSa5niblq0JXK1UDdFoxFEmo9rviS1XmsFBz1QQcSuuKH6XYlcd7eaQAWuG5WYOggkB4B01ui5CIknwj+CVFoPPSeZ0q/73QhA0g0XN5Qoccb9xLP3/EErmHiWHj7RaMqsyo0YLBxLQiOP3/wXLXuMzRS7zitlIl3Xa66QvU2kw5G5EpmVKoYXoPuSeMFh8mJ+a+a1EKEzoITWqld3XT74pb/jsb/5ErrXXciWmsaRCxcbx/qMX8qTWhP89D0fphJP4msavq5z6dYzPPXpTo3UA4AQ5MbizJ7OsjKZYGk6xepErBXIQQULXxcUhtVnWM5EuHJmiMVjKRZOpJk/lcFvsMYrSYtAF21vm+z42byma+ttDomRcrgSQUv7q/FTA5Lr9a5jNalSj6mVcluK9FC7ae4Sg9TWAcCyNCaObAg2gjIKPDpto/XIxY+Om9SqAU59o73FNAXjk4ejQ+Sh9Vf5pv3+Vo0ElFnVnflzGPLqVmWe0LkUm6SuWRypLZEOCVqV//FfgfbPqSRtsksVpL+x8pSoGkilwSRO5erdOXrUbsao+3j2xmq+lLaxy65ivQM0Oo2WjyZbOzDD8Yl2FIkFqlCfyNXCZeilxC67oZOQFOq+AI989escO3e+5wpQrfS1Vm1Ib6Tt8iOT/OhnfxHNd5m5ZRgvcm1Z1L6hUU2q11SPmbi2QWpVBd5q3Oo2ltJEuGyIJlg4nmZooUy0odZbTZjks1EyqxUiFQ8EVJI2a+Oxtl1yTyWCHUAA6ZUauidZn0gAUE5aoTthKcS+W/1eK9yYr+o6RCptkEjq1KoBQggiUbHlzkJvmGJVKyqYWLYgGtu6Xfh6wrHqIo8u/YhnR95FVY+gS597cm/z0PprV3XdZTvLlycfVRwN1Er09sI7PLL6YtuE8NLXDJ7+qfIqWTieZni+hF1VK/hazGB1cqN4HSYeCOoP33DbAwlCsHokSaHmYVc9fEOo2oVQefVYsd5TflylQzylX92BWNEhma+1jaM5D+WHozhRE6taZfrceXS/dyAWUjJz6pQKZH572kYIgW9aRGoBpf3NLu4YTtRk5ejuFkm+qbN8LNVlhrUUT4cbZAWSWMkh0ERXS2+veo1sVPBDazmonUl+NEaga5QyEeJFpxVMAtRFQxsmbhAMAskBQtPEjnS7hFDHxw4pMfp0eYZT5RlcYbT0sq4GAYKvTXwAR29fTb+VOsnR6iInKu2an81diWfpLB5Pt6QsOoujtZgZuoLUpOxZPHcjRlsHjlnzGL9cUOq/PV6mRKVXwpAMYYELVEqmaW4UL5Tb6zAd1/YNg2c++Qk82yJa6pbBV69J7ZhuSIS9Nx2PmfXG5xTIVqRupioF4OkC3ZNtO75AQCEbIZWrQxAmH6pONpwAJ6qBpjq0oiWXSNlRXKO0fUOrPw8CyQD7CgF9ux1uhyV7qC1V1oSnmbyROtUVSF76msFT/+H7PPZf3g90B5AmitkIyfWa6oZrPNacwPsSW5SS0dliV+G2c3UrBRR7dINpIe25red8SaAFxHPh6+UAWJ6a4ruf/QxOwwvdiRihBLpAsKP0ilnzSK9UsGs+rqWTH+nR8rpHsKoe0ZLqjGop6EqJVfOwax6eqSsC4C5X9qOzxa6dWiChMByhmI0S6GKjdbexCylmIuRHY5SyEcYuFzDdbtl5pQrdTkqtJq1DLcS4EwwCyQCHBoHQevI+fBG+2utHh0v5SKTJLFeIll3FEchGehoSiUASz9WIll08U6OasEI9LTaT8DxLY3Ui0SoSd6KSsDDWu3clUghcW1deJ2i8c8eDnH79BfQGySgAPMvi+5/4eCuIANRjBq6tt3FeAlSDQaXPyc2qem2EQt0LsK+4rEwl936ClJKhxbIiYjbGm16tsjYWI1F0sBppSRo1oIXjqR2v8A3HRw8JAhrKiTHfkI1fm0yQG4uhuwGeqbXkWnxTZ3UyzsTl9iaMQCiSa6ey8M2EQSAZ4NBgrL4auhI1ApczWzDm//e//Y/8vPbPt7y2b+p9uRh2ivpJVH68V9bONTUWT6S3nWSKw1HFvPc2rtvUoEII7KpKvc2dvJ1aLMH02VeIVMusD0/w8vveSynTESiFYHE6TXqloiZnoJy0yY2GW76GoYvTgtrhZBfLVBN97AqkJFLxiOeVtHs5ZVPrsZuwq4rN38mhGV6sINnUXipBBAEjc6XtWeo7QefOTde6PjMRSEbmy207TYmSX1m7SYU5mxgEkgEODQwZ8Njic3xn/GEkgkDTMQKX8doqtxR7B5KXvmbw1Y//m22DST9IrrdrPzUn1xYHZdOxTWJjPyvVQNeYP5Ehka+1NLyK2UirDuPYOtGSqnGsjR9lbfwoNO5p12D0SoGVqURr9QwqlZcbi5PbTvW2B6weOllNH/utODWgAlEiV2/taGJFh0rSZnWy2+sjVqj3rC11vnsCFXiEH7S93u3gmSo4aB3mVmpHsf0OK5GrKaXizrHUfZV+3EM31cOGQSAZ4FDhZGWOX77ydd5OnqCq20xX5jlWWdi2kP/S1wz4hau/f6wYzmxvTqpNQqNs1CK28uvuuoauZDeKQ90aX6VMhPRaVemubXq8+Xuk7DIyV1LdS3sE39DQ3HBS5nZBxKx7JHLtOwzleV+nmLVDWnl3PglvTh32d4Jg+UiC8SsFpdorN/glYe95JzpbupuQAqX71aen/I2IQSAZ4NAh5ZV31Ub81eDqdyVyC1XfhekUdt1H9wLqUZNazNizds/A0FiYVm3MVki7sgZEKy5aw09e831OvfY6J994C9cyefv++5g7eWJH9ywMRcgutUuQBEI1J2z3uiIlN3SWFxLi+XpXIKnFDJK58GsF0KV95dq62ulJSTxfV/LvvqQe0cmNxXs2FDhRk9nTWeL5eutz6itNB1vofoF/E9dHYBBIBriJsBe7kkI2glXt1oryLB03auI2J0gpiVRcDCfAtXXq0asPKlIIcqMxhuaLmCEdvFIIdC9ACslH/uIvGVpewnRVemrq4iXeePABXvzg+/u+XykTQfclqdVqa/lfTtvkRkMIlZ1j0UTPLUMyV8d0fJaPpFqBuUXw7LwODZtib8NoCiFYmVTkv9RqlfRqtfV5RCoe45fyLBxP9xRIDHSN4lCUWMOtcWQ+UAFoNN4m6NiJYjZCvNCt++WZGk7kxm3t7QeDQDLATYV/+ZU/4vdDpOb7RVMrKrVeI2jMlb6usXRko1CveQHjl5W0eROurbM4nd6V0ZVR9xm/oljqzTpMaCOwlLiWzvG332ZoebkVRABM1+XOHz9PpFzGM00u3nEby0eObH1jIciPxCgMRdHdAN8Q3TWJMMIfUElZZJe6daiaR9lVj6HFUqvBwar1YJhrsDyVwHICrJqHZypORqBriEC2BZHW9SWkVyqsbOFumVivtu22ohUP+3Kexel0z2DiRgxWJ+IML1ZoKDHiWnqbqsHNikEgGeCmgQTmI6M8MbXEMy/GKaftnct6N7SiCkNR7KrymujcbQwtlDCd9jZTs+6TWSq3ZDT6heH4TF7ItemANV/L5mASCFgfjYEmOHbuPKbbza7Xg4BbfvoqAGde+Slv338vL/zsY+E3lpJ4oU48r8QiS5kIFatdfTi5VlMTeSDxDY31sVjLcjbQNZaPJBmdLbaK7ZuhSeURshpI0ASepXe9Z6BSYb6pU46aLWJm6/V44dwbQbsnSdhryyxXuwmgEjLLFZamewegSjpCJWVj1X2CxrgHGASSAW4SSOCZkYc4lzyO9x1BStRI5mrkRqIUw7SvtkFgaOFcCimJldzwibPgsL4DA0eA7EKpLYA0IQBfUxO2b2jkh6MtH/NaNEYgRJds/ObraJ7HbS+9wvm772J9bKzrNYzOFFsmTgB2tUS0ZLV2EJ0pJcMLGJ4vITXRKjrXEhYzZ4Y4enYtvCNLKvWAAEF+OEqkQ2ssEA1RRiO8/uBvUa9ytzB/0z0ZKp4ooGF2tg1uYM2s3eLmrhANcNNgMTKigohmgNCUqquEzEp1W3n3vcJWyq9WzSO5VlVtsJs8wLcUFRSCudNZFo+nW0EE4Ox993TJxofdWfN9jp073/W4XfHaggg0O66UfhRSkg6RdNEkpJfbJeylJqjGzdD7e6bWMhBzoiYrR5J4huq/ayoLrG6xg5N6I83V8QYFglA/9ya2CkBej6A1wNYYhNUBbgpciB/pMtpqIlpyKWW7n9O8oCXM6ET6LJYLleqyq+0BQKLY612QkpHZEtHyRrFZig03PakRatohUdavYciPDPPsRx/n4W9+Cyk0NN9DD/NW0TR8o3sKiFSc0B2EkGA32Pybg91mmCHtwrmxOJFKHhEoDasW2XKiXcSwmrCYPW1ueKv38X4rrxJBMldTaTBDY20strWMiyYoZiIkO3xDAgH5PhoJBujGIJAMcFNAD3wEkjDJPdm5CJWSzHJlo6AuVefQ4rH+ZDlWJxNMXNyYOAMBgS5CiYGJXI1ouZ2fIBvaXXOnMhSyUZVC2jw81EScG+s96V24604u33qGsdk5dM/jQ09+GaPDv0QKuHjbbV3nBroWqtMlG68j0NQ/PSyYSEmsUG/VSkB1tM2fypBcq2JXPVxLpzAUbVdVbkKILVusw47PjcfJjcV2FIByYzEQNKRnlK3A+mjspuaCXA0GgWSAmwJnSpd4JXMbvuhOXXROHrGioyYYCXqzKckJGJ0psnCyt2ZXE4bjE+gCI1BdVrWY2cU6byKR7zZMaupaGU5AYSSK5fhEi04rBHqGxuL09kHNN03mTxwH4Psf/yjv/9o3CIRosPEDnnv85yinuwvL5ZRNpiNF1RxYJakk83Oj0S6OCaj01vB8Cc0LKG0i+fmG1pthL6XSBAukEpvcRWfbrgLQWJzcaEyx0vX+AtAA4RgEkgFuCmTdIu9dfYnnht+FIGi00Ar+6dHv83v6L7UdmwwRTxQov2/D8bfs1LGqrlKY3XR+pOKSWa6Edmxt6aaHVJyJI0l018esq3vvplPo0h23M3/yBEfPvwPA7KmT1KPhbO7A0Fg+mmRktqTGIFWtY/lIshUMS9koUgiGFstdXVmahOxyBavmKQn1TKTnmA3HZ2ymgO4GaiKXkrXxOOUeKsl7DiFuammTvcIgkAxw0+DuwnlOlWe4EptEk5LpyhzBBZf7/jjXpg6s9cj/I0TP2kAT6ZVuHxBNQjJfpxozldJsoY4WSMopm1LSIuN0t6IGmsDdNPn6pr6xA5FyV6tnJxLhnbvu7OvYWtxi5kwWu6I6qWoxA7T2HVU5EyG7XEHzQzqgJCQLDhJIrddYnUy0pbuar2PsSgGjqcjbaEYYWizjRoxBZ9QhwuCTGuCmQsyvc1vxYttjn/utP4c//tVWMKkkLIyQyb0pzbEVTCfcbREJY3PKEngzKc+JGDiWjuX4G8xtYOVIN8ktlq+RXa6ie4ocmBuJbblyNxy/0Syg7VyuJVCy7olCvWVNvD4e7woGrqm3JO03Q2z6KRrprmrCaktbWTUvXH5fQmK9xtrk9pwbzQtUo4JUKcpercIHDavmYTXe+34lWA4zBoFkgAGAz99a43cbvxeGlBRGp6T72kS3am0nHFvfWGFvQthZmlQTzkpTKr7i4huCcjrSNSHGCnWGF8qbeBuylVYqdQpDSrlhztRAoKu6Sr9psZH5EtGS00pbab5keL6Eb2htHVH5kShWRyovFALsqkstvlGP0j0ZKqPSrBFth1i+xvDCJvb8Yvlg02Jh2MTBARr+KUrS/0YmL14f4XuAAa4xao99kfueUKqBUteYP5khNxqjEjcppW0Wjqe7UzMhyI/EtlXG3QxNKlOlasIkMASpXJ2pCzmGFkptcueZ5fDCdmaluygeL9SJF1QRv/lP9wJGZ4tdx4aOyQuIhSjdCqnMpjajlrBYnYjj6cr/fKt40mkTXI8aoTWiANQqfgvort8KrJv/DS2WD4wXFIbkWq3FwdEkaIEKmCNz/b33hxWDQHKAqFYD1lc9inmfYJtc+wAHj8/91p+3fpeaaAkUro/F+pZScSMGi9Mpag2r2+0+ZQn4hmB0tkh6pYrhBui+JJGrM9loIQbadLs2Q/MldNj09moWMBwfPcyvvaGgO3khx5FzawwvlELH3bxGJyrpCLO3ZJm5JcvSkUQY7QWkChz86SVwAAAXHUlEQVSbERgaueFo2/FN2Zd4wUGE1F6aiBXDRR6RECv0eO4AkMyHv/dWQxX6RsUgtXUAkFIye9mhUm58kQRoAo6dtLHtQSy/nvCH/2KB3/0/xxlaaNQHGqmXYibS4B5sv91woiaLJ9IQBEy/vb7lsVJALWp0Tf4qnRQQz9coZaO4loblhE9EiXydUnajA2urhgBNSjpDQWa50nZ/vdSt0wVqku8MBhs3FQS6oBY3kZpAdvjXI5WsitkIROV0hFrMoDASw3B8EgWnTcLF6hB17LqdDO94UzWZa7hI63FrCT1tom8EDGaxA8D6mkelHCCl+i7JAHwf5q5cu5XTAOGoPfZFPnNiuSUXrgWNrqtcjeR6bUfXsmt+aJqrKbgYCFidiKP3WKhqUkmkAORG4z13CZ3ppkqyWzYE1C7L7cjTa34QGsSaY2wbs7a19AgoZruQ3bRPgZKjSRQc4gWH0ZkCw/MlRmYKrSDSNi7UroQeQbGSsMLfW8He+8nvAJWkFfre+4bSRLtRMdiRHADy637oYsR1JK4TYG4hMDfAwUICr3xNdna6Km7EkuJG5EZjfTHczbA0EmpSrcYMlo+mkJoqsoeh6d4HW0+Outf+5SoMRYgVHQzXb2sWWJlKdO2ozJofWvDWANcUSKGh+wGuqaH5kolLeepRg9xId7rPcHyyjQaAsNe8+XchG4GC8EaEzddM5mrYVQ/P0ikMR3EiBp6t2PGptY12aymUZ4hrX7tpLT8cJVpyW+990Nhmhb33NxIGgeQgsMWO9gbe7R5KBGg9NbmauftoyWXuVEZ1VknZkxnt9GgVDkRjRd1oha1HDTxTC5VRL6U3OpA8UwvVsvLM9qgndY35E2nihTrRhjZWqQcp0De10O+nSmOZrE4lu707Si6Rcrt5lFH3mbyUQwThgaFZ++jEdlPr5KV8q3PMqvtESw4rR5JUExb5hqRJrFBHoHzXuy18DxaqUSNNrOhgV9yGf0p3F96NhmsSSIQQQ8B/Bk4AF4FfllJ2JZOFED7w08Z/L0spnzioMe4lUhmd1WWvK2johsC0btxVymGETkDaLZK3wj0pBKoGkVqr4lq6IuQ1pFCK2YhyD2wEFKdBqrNqXmsSViki1eK7cVHVHjoyV1JtowJcU2N1MqEm+gbWR2OMzLe7M7Z8SDqhCcqZSGgrrOYFxAt1DDegHjVwIjpW1W/X8xIoH/MQ7w7ReCGZlQrLDfOozEqlZxAJ2F0QAdpY882dzNBCmdnTipvhRI0tXQ2vCYSgkrL76vK7UXCtPoHfA74jpfyCEOL3Gv//n0KOq0op7z/Yoe09ssMGxYKP40hkQwkCAVNHLcQNvN09rHj/yj/wjYkP4AkNQrS5NCBacki6QWuCFdCqobQ0pYRg6ViKzFJZdSFJSTVusj4e79KFCgyNpekUwg8QktAVbDVls6IJMsuVllRLbodCg1bVY/xKvuEFAkFO7WhqcYNoxWsFutWJBE7EQHf93t4d1Q0iYqfacRMSKKUtVQfZxe477Jq6H6hdYB/SJpGyQ3axgtnQP8sPR/vynB9gZ7hWgeRTwKON3/8UeJrwQHJDQNMEx0/ZlIoB1YqPYQhSGQNjoPFzXeJodYknZr/Lj4fvYSY60TXpSBQvI4zXkVyvte1KpCZYn0j0bWgldW3LluFqwtq9Qq1UfAZtU3ZMk6q1uJJQplWi4XbYHH8QIjTZxObdkmdoGGHtrUIF1nrcYni+1IgMotF1QpeqcavQ31AaNrzwd6MfYUe74jI6s0GW1H2l6qz5ciAXv8e4Vom7cSnlPEDj51iP4yJCiBeEEM8JIT7d62JCiN9sHPdCzr8+O6GEECRTOmMTFkMj5iCIXOcYddb5hflnmKotoQXtRfNmS3AYmizw6xG6F4RyGZq2t4GuqSaCTYGzyafZzjyqMBINPaactJC6RiVlM3NmiJXJJCuTCWZuyZJvnBMIlf6qR3QqCZNCNsL8yQz54Vjva/YRSHqROFNr1Z7dYAPsDvu2IxFCfBsIW4f9zzu4zLSUck4IcQr4rhDip1LKLks3KeWfAH8CcHs0M/iGDLBn+MjCD/je6Lu5FJ8iMHQ8obE6ESe1WiVa7daYCjTFp7hWEL5E9wNVgO9M3zQk5HeKtXGVqmv6t0shWB9rT6lVExbrYzGyy1VotP9Wklabw6HURFv3WWEkRmEoiuEF+LroktkvmRqG66uUYUMZuBYzWevT975X1xyo9Jiv3biSJQeNfQskUsqf6/WcEGJRCDEppZwXQkwCSz2uMdf4+Y4Q4mngXUC3N+gAA+wT7MDlI4vP4ggDVzP4u3/7GWb/ziLQBfblQnjh+1rk3zv1tYRgfSTa5QniWDpWvV1YMhBQzGxRGBaCtYkE62NxND9oS31tRikbpZSJYLjhgSEUmuitQdXwDCkMRzEcX3Ex+mi7bsKxdaKVcA92v5+xDdA3rtW7+STw+cbvnwe+1HmAECIrhLAbv48AjwCvH9gIBxhgEyzpEfdr/Mpv/wXQYK9Pp6hGDXxN4Ng6K1OJayYYOLRYbtfXCiTZ5QrRYr3tuJWpBL6mUknNtFItaqoOrW0gNdGV+uqCUIGhryDSJwJdw4maOwoioFJvYamxwlBUSUsMsGe4VoHkC8DjQoizwOON/yOEeEgI8e8ax9wBvCCEeBl4CviClHIQSAa45viXX/kjQAWTpeNpZm4dYv5khmry2rR7ikBpZYXVA9IrDda7lKRWKkxeKqAHKihUEioYLk+nbsgupnrMZPloEsfSlaaZLsiNxsiPbB80B9gZrknXlpRyFfhwyOMvAP9t4/dngXsOeGgDDNAX/uVX/ojf/4Xf2Zdra15AdqncEiasJC3Wx+I9SW2a31sMsNlJlV6tklrd4IPogSRWcq+K62A4PumVSot1nv//27uz2Lju647j3zMbZ7hvWkhZG5PAjhOjqeG6SZQWsRsUsRHYTpMA6UOTQCkCowjaPvTBQNECDQqkaZE8BG1RuK2BBE3TLHZcN7bixoncwLDsOg1kybIjx5IXUaREkRJ3znCWfx/uJcVlhjPDWe4d8/cBBI04l8PjP+k5vP/lnIHUuhLziXSO3omF1Z4os/1J5nubu/U23ZFgfER92BtNE4Ui27RyZ1JXzitD0jG7vDpN1TG7zN43Z0qWQcjHIkV3Ma0WWXTeAcqiZeivLG36vErEMjmG3pimY3aZeLZAciHL7guzpPw1mngmx543Z0gteocx49kCfROLm+qCyduDEolIDY5/4pm6vl5qPks0v75UiuGd9ei/NF+8sq8Z13atXw9YOYsxPdhOpOCwEjctsdz2enf0XVl/kt243g8E5+i5sli05XD31FLZdsXSepRIRGpw4uipur5ePJMr+qZvQMfMMkOvT2NFprIWepNc2ddFOhkjF/PWPy4d8mphbbUleTmxvdntUifZIwWv9tjGnWFrRUv0VpHWpUQiUqN6TnHlEtGSHRYjeIcKS5WzT3cmuHyoh4vv7Gfyhu7rVXCL3LGAt4Npend1J7xjmWVGzrzMvvMv0zFbvNeKixi5eLTkCf18Ew/jdsykGT53jQNnpxh6fZrkQjgPLLe6kFU7E2lN9Vp8X+xK0DcRwXKbKwHD9TWT2TJ9QTZa6E3iIkbP5CKxbIFsW5RruzvWLY6Xs+viGB/53sOYc0Tyea+W2PBhzr7viNfYymChuw0XMWYGU7RdyK6b3ioYLPS01XVr8FY2Vi1OZPLsGp3jyg3dpDuCrRL8dqM7EpE6qcudiRmXDvWQbo+V/I1+uyfnF7vbGB/p48KNA1w61LtlEolm88QzudUFfisUuOMHj5JYXiaezRItFIjm8+wae4OBS2+tNpRaOQWfaY8zOdxJLhZZbeI115tcfb7Rotk8fZdL9LmfWGhKDDuJ7khE6qgedyb5WISJAz0Mnb+2qUdJwW/etI5ztM8tE8/kybZFWexMbPvAXTRXYHB0jkTGOxG+Ugm4c/YK0SIL87F8joGJ85z8rfdt2p681NXGxc4EVvC6KzZr2280m2fo9ZmSazRblU6R7dEdiUid1WvNZGJ/N7l4xDuBHvF7hPS2sbimXlUkV2D4/DQD4/P0TC0xMD7PvvPXiGa38WbpHLvfmqHN758ScV7F3MGxOe/upPQnlm7cZOaVzG/i2ZGeySVvp1qJ53NVnpCX8pRIRBqgHskkH48yNtLLxP5upvZ2cnGkl+k961u29k0sEPP7oqxswY3mvLpb1Uqk88Sym9dmzEGmrbdoMsjG45x773uq/lqNlFrIlkwiBfDK/EtdKZGINEi91kwy7XEWu9uK1ppqn1ve/MaP92ZabR/naK5QdMeYAfGs45mP3kUuFiMX9XZkZeNxLu+/gdfffVNVX6fR8iXWkBxwdU/7ugrEUh9aIxFpoEaWUqm35VRs0+I0eG/A8XQerJdn7vokXdMXSWTSjB0+yKUDB0JXp2t2IMXAxpbEQLozzkKf6mw1ghKJSAtb7Ep4bXzXfMwBS53ejqzOa0v0TKWJ5gpkE1Gu7W4nXaLDYj4WYbY3Sdd0el2Peb8zNDhwlmRi341MHOhp3H9UjRa7EsSXU3RPLa32Mcmk4kwOVdbHRKqnqS2RBtv2FFfB0Xt5gf2vXuXAL6fY/dYsscz6RfRrezrIJbwF+ZVttvlYhKt7O+m6mqZvYpGYfyYlsZxn18U52hayJb/k9O52poY6ySRjFGxzz3QDkks5IsXa6oaFGTOD7Yy+s4/L+7u8daYD3U07v7ITaWRFmmA7yWTXxTnv7sDfgZRczDL05sy6N/FCNMLY4V4mh7uY3tXO5HAnF9/RSz5q9E6VKtS4WPqLmrHY3calQz1eA6siHFtXHA4Lt80+JlI9JRKRJqkmmcQyeZKL2XWJwJtecptLpJjXwnZ2IOX1RDHz+saXWGyv9BzFUkei6KFIZ1t0NZQdSYlEpImeKHy9ouviy7nN80p4dxSJ9FZnOjyFaJF5KV+2wiQwM5giH7XVGl0rU2dX93aEboFdgqVEItJEJ4/FKkomuUSUYrcDBbxe5GWZMdOfKlqocWZXZTuXCrEI4yO9zA6kSCdjLHQnuHywp6ZmWPL2pEQi0mSVJJNsW4xMKrapxwgRY77CLayzAymmd7WTj5p/7iPC5L4u0h2Vn6MoRCPMDLZz+VAPU8NdLCe10VM200+F7BjLFuOF/lt4resgDhiZv8DtV0+TLDS/tPjJYzGOP/QMdzz8oZLXXLmhm76JBTpmMt7p8lSMq3s7yMcr/P3PjLn+FHP9KW+9RNNR0iBKJLIjOOCxfXdyLd5NIeJNDZ3tOsxYag+funCM0t0zGufE0VMcf4iSycRFjKt7O69XzK0lESiJSANpakt2hNHUHmbjnatJBKAQibIYS/Jmx77A4jpx9FT5dr3W3KKHItVSIpEdYaqtl5xt/nHPRuJMJnoDiOi6E0dP8Wv3TAcag0gtlEhkR+jOzhNzmw/RxQpZunPBNzr68qPfDDoEkW1TIpEd4eDCOIlCFitcTybmCsQKed4x/1aAkXlOHouVn+ISCSklEtkRohS4b/QphtMTmCtgrsCe9CT3XXyKuAtHx7yK1ktEQki7tmTH6Mwv8bHx/yFn3h6tsCSQtcrt5BIJI92RyI4Tc/lQJpEVJ46e4um/Ud8MaR1KJCIh9OwtX1UykZahRCISUkom0iqUSERC7NlbvsrX/uxS0GGIbEmJRCTk0nc8omQioaZEItIClEwkzJRIRFrErYOHgw5BpCglEpEWocV3CSslEpEWosV3CaNAEomZfcrMzphZwcxu2+K6j5rZWTN7zcweaGaMImGl9RIJm6DuSF4Cfg/4WakLzCwK/ANwF3Az8PtmdnNzwhMJNyUTCZNAEolz7hXn3Nkyl90OvOacO++cWwb+A7i38dGJtIb0HY+oj4mEQpiLNu4DLqz59yjwm8UuNLMvAF/w/5k58tLjLzU4tnoYBCaDDqICirO+6hvnkcfr9lIb7MzxbIxWiBHgxu1+YsMSiZk9Bewt8tSfO+f+s5KXKPKxoo21nXMPAg/6X/fnzrmS6y5hoTjrS3HWl+Ksn1aIEbw4t/u5DUskzrmP1PgSo8D+Nf++ARir8TVFRKTOwrz99wXgXWZ22MwSwKeBxwKOSURENghq++/HzWwU+ADwuJk96X982MyeAHDO5YAvAk8CrwDfdc6dqeDlH2xQ2PWmOOtLcdaX4qyfVogRaojTnCu67CAiIlKRME9tiYhIC1AiERGRmrR8Iqmi3MobZnbazE7Wss1tu1qlLIyZ9ZvZj83sV/7ffSWuy/tjedLMmrYJotz4mFmbmX3Hf/55MzvUrNg2xFEuzs+Z2ZU1Y/iHAcT4kJlNmFnRc1fm+br/33DKzG5tdox+HOXi/LCZzawZy78MIMb9ZnbczF7x/z//kyLXBD6eFcZZ/Xg651r6D/BuvIM0TwO3bXHdG8BgmOMEosA5YARIAC8CNzc5zr8FHvAfPwB8pcR18wGMYdnxAf4I+Cf/8aeB74Q0zs8Bf9/s2DbE8NvArcBLJZ6/GziGd6br/cDzIY3zw8APAx7LIeBW/3EX8GqR73ng41lhnFWPZ8vfkbjKyq0ErsI4w1AW5l7gG/7jbwD3Nfnrb6WS8Vkb//eB3zGzYodbGykM38eynHM/A65uccm9wDed5zmg18yGmhPddRXEGTjn3Lhz7hf+4zm8nab7NlwW+HhWGGfVWj6RVMEB/21m/+eXVAmjYmVhav4mV2mPc24cvB86YHeJ65Jm9nMze87MmpVsKhmf1Wuct4V8BhhoSnRFYvCV+j5+wp/i+L6Z7S/yfNDC8PNYqQ+Y2YtmdszM3hNkIP506q8Dz294KlTjuUWcUOV4hrnW1qo6lFsBOOKcGzOz3cCPzeyX/m86ddPMsjC12CrOKl7mgD+eI8BPzey0c+5cfSIsqZLxacoYllFJDP8FfNs5lzGz+/Huou5seGTVCcNYVuIXwEHn3LyZ3Q08CrwriEDMrBN4GPhT59zsxqeLfEog41kmzqrHsyUSiau93ArOuTH/7wkz+wHe9ENdE0kd4mxKWZit4jSzy2Y25Jwb92+7J0q8xsp4njezp/F+s2l0IqlkfFauGTWzGNBD86dFysbpnJta889/Br7ShLiq1RJlita+ETrnnjCzfzSzQedcUwslmlkc7835W865R4pcEorxLBfndsZzR0xtmVmHmXWtPAZ+F68nStiEoSzMY8Bn/cefBTbdSZlZn5m1+Y8HgSPAy02IrZLxWRv/J4GfOn8FsYnKxrlhbvwevLnqsHkM+Iy/2+j9wMzKtGeYmNnelXUwM7sd731tauvPqnsMBvwr8Ipz7mslLgt8PCuJc1vj2exdA/X+A3wcL9NngMvAk/7Hh4En/McjeDtnXgTO4E01hS5Od31nx6t4v90HEecA8BPgV/7f/f7HbwP+xX/8QeC0P56ngc83Mb5N4wN8CbjHf5wEvge8BvwvMBLQz2W5OL/s/yy+CBwHbgogxm8D40DW/9n8PHA/cL//vOE1lzvnf59L7ooMOM4vrhnL54APBhDjh/CmqU4BJ/0/d4dtPCuMs+rxVIkUERGpyY6Y2hIRkcZRIhERkZookYiISE2USEREpCZKJCIiUhMlEpEmMrMfmdm0mf0w6FhE6kWJRKS5/g74g6CDEKknJRKRBjCz3/ALMib9ygpnzOy9zrmfAHNBxydSTy1Ra0uk1TjnXjCv4ddfAyng35xzYSzLI1IzJRKRxvkSXt2tNPDHAcci0jCa2hJpnH6gE68TXTLgWEQaRolEpHEeBP4C+BbhLBMvUhea2hJpADP7DJBzzv27mUWBZ83sTuCvgJuATjMbxauc/GSQsYrUStV/RUSkJpraEhGRmiiRiIhITZRIRESkJkokIiJSEyUSERGpiRKJiIjURIlERERq8v+pGcpwb5SLPgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, beta = 0.9, optimizer = \"momentum\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Momentum optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.3 - Mini-batch with Adam mode\n",
    "\n",
    "Run the following code to see how the model does with Adam."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690843\n",
      "Cost after epoch 1000: 0.624609\n",
      "Cost after epoch 2000: 0.584592\n",
      "Cost after epoch 3000: 0.561816\n",
      "Cost after epoch 4000: 0.558931\n",
      "Cost after epoch 5000: 0.542699\n",
      "Cost after epoch 6000: 0.547005\n",
      "Cost after epoch 7000: 0.528101\n",
      "Cost after epoch 8000: 0.548008\n",
      "Cost after epoch 9000: 0.561397\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.9366666666666666\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"adam\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Adam optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.4 - Summary\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "        <td>\n",
    "        **optimization method**\n",
    "        </td>\n",
    "        <td>\n",
    "        **accuracy**\n",
    "        </td>\n",
    "        <td>\n",
    "        **cost shape**\n",
    "        </td>\n",
    "\n",
    "    </tr>\n",
    "        <td>\n",
    "        Gradient descent\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Momentum\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Adam\n",
    "        </td>\n",
    "        <td>\n",
    "        94%\n",
    "        </td>\n",
    "        <td>\n",
    "        smoother\n",
    "        </td>\n",
    "    </tr>\n",
    "</table> \n",
    "\n",
    "Momentum usually helps, but given the small learning rate and the simplistic dataset, its impact is almost negligeable. Also, the huge oscillations you see in the cost come from the fact that some minibatches are more difficult thans others for the optimization algorithm.\n",
    "\n",
    "Adam on the other hand, clearly outperforms mini-batch gradient descent and Momentum. If you run the model for more epochs on this simple dataset, all three methods will lead to very good results. However, you've seen that Adam converges a lot faster.\n",
    "\n",
    "Some advantages of Adam include:\n",
    "- Relatively low memory requirements (though higher than gradient descent and gradient descent with momentum) \n",
    "- Usually works well even with little tuning of hyperparameters (except $\\alpha$)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**References**:\n",
    "\n",
    "- Adam paper: https://arxiv.org/pdf/1412.6980.pdf"
   ]
  }
 ],
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